Let’s get this out of the way to begin with, “My name is Thomas, and I’m a Cody Lewis fanboy.” Out of the DM/GM Tip people, his videos are the ones I will faithfully watch since I discovered his channel several months ago. “Cody, you’re still awesome, but I gotta say you’re wrong on Alignment.” If you don’t know what I’m talking about:
In his latest video, he explains his rationale for why he believes Alignment to be a broken, D&D-mechanic that has unnecessarily influenced other tabletop RPGs and has limped along in subsequent iterations of the game. Now, please, go check out his arguments so you hear and understand his arguments directly from him. I’ll be right here when you get back. I’m not going to attempt a point-by-point refutation, which is why I want you to listen to Cody. But in the end, I think there are two fundamentally important points he gets wrong: 1) Alignment is not a binary mechanic (Good vs Evil and Order vs Chaos); and 2) Alignment works to enhance narrative development not detract. And so taking a cue from Cody, “let’s talk about it.”
There are a couple of points I want to draw from the Player’s Handbook. When introducing the idea of alignment, the PHB uses terms like “broadly describes” and “typical behavior.” And immediately before defining the 9 Alignment profiles it warns that these are not meant to create static PCs or NPCs, “Individuals might vary significantly from that typical behavior, and few people are perfectly and consistently faithful to the precepts of their alignment” (D&D5e PHB 122). Despite the direction set
by the Player’s Handbook, when most people think about Alignment they are drawn to those memes proliferating on the interwebs. Those nine, darling little boxes have the potential to create flame wars across continents, break-up families, and-according to recent scientific discoveries-caused the extinction of the dinosaurs. No one can agree about who goes into each category. Why? Because each person placed in one of those boxes breaks the mold they are being forced into.
The characters we play and create are too complex to fit THAT model, but that is not the classification Dungeons & Dragons created. It is not the mechanic that is broken, but the regularly-perpetuated-because-it-is-easy-to-digest-but-incorrect mechanic that is broken. 
Yes, we have the 9 Alignments, and we have the description of the Alignments; yet the game mechanic is more fluid in its approach, the PHB does not introduce a grid. It’s not as fun to look at, but a better chart omits the character images. What I really appreciate about the Alignment grid to the left is that the way it depicts Alignment is on a continuum; not everything is equal or rigidly regulated-no chart. An individual can fit comfortably in the Lawful Evil category, still be able to shift toward neutrality, goodness, or chaos, and maintain their core identity. The alignment structure is about the player character’s core understanding of the world and his or her interaction within it.
5th edition devotes only one page to alignment, whereas AD&D2-my first D&D experience-devotes 4, going on 5, pages of material. Others have argued that the subsequent editions have tried to “loosen the straight jacket” imposed on Alignment. However, looking at these two editions the same basic thread remains. Despite the regular use of the masculine pronoun, the AD&D2 opening statement on Alignment can just as easily fit into 5E’s PHB:
The character’s alignment is a guide to his basic moral and ethical attitudes towards others, society, good, evil, and the forces of the universe in general. Use the chosen alignment as a guide to provide a clearer idea of how the character will handle moral dilemmas. Always consider alignment as a tool, not a straightjacket that restricts the character. Although alignment defines general attitudes, it certainly doesn’t prevent a character from changing his beliefs, acting irrationally, or behaving out of character. … These nine alignments serve well to define the attitudes of most of the people in the world. (AD&D2e PHB 46)
When alignment was introduced in Dungeons & Dragons, the game was mainly about Dungeon Crawls and less about story. The typical hook was there is treasure, a monster is guarding it, and go get it. Character background and history were not as prevalent as they are today. The only game mechanic that governed roleplaying was Alignment. If Alignment is the only mechanic governing character interaction and the players or Dungeon Master only allow a black-and-white interpretation of it; then and only then does such a mechanic suck. The choices real people make fall on the myriad shades of grey, and our experience of those moral and societal choices should be reflected in the game. Since the beginning of D&D there was an attempt to recognize that choices are not binary, and the three original alignments were established. I don’t have a copy of the original D&D rules, but thanks to Wikipedia I can find out: lawful, chaotic, and neutral. Lawful and Chaotic imply a PC’s bias to order or anarchy, whereas neutral was meant to be the attempt to find that middle ground. In the next few editions TSR attempted to refine the roleplaying mechanic, adding a moral component (Good and Evil), and again understanding that two choices were insufficient they added neutrality. In the end, it’s a game and it’s not possible to create an unique alignment descriptor for every possible character, which is why the mechanic is defined as a continuum. The grids, not the mechanic, are what is wrong.
With the addition of a Background mechanic in 4th edition, Alignment no longer had to structure the totality of in-game interactions. Some of the older work of Alignment could be passed off to Background. Background was able to provide a greater flavor, but Alignment remained the overarching worldview. The system was not just about creating a backstory, but the backstory impacted how the PC lived in the world. 
The introduction to Background in 5th edition explains it this way, “Every story has a beginning. Your character’s background reveals where you came from, how you became an adventurer, and your place in the world. … Choosing a background provides you with important story cues about your character’s identity” (D&D5e PHB 125). Identity of the player … that’s how Alignment was meant to be used, but Alignment alone became more difficult to use in the ever-growing narrative world of modern RPGs, hence the creation of Background. The connection between the two is inherent in their relative placement in the PHB. Alignment provides the larger motivational framework, whereas the Background provides the peculiars. With the expansion of Background, does that mean that Alignment no longer has a place? There is still a need for a larger macro mechanic to provide a direction.
Of course there are going to be people who feel that having these labels are too confining for them, and they just want to play their character however it feels right at the time. *cough*cough* Neutral *cough*cough* That latent feeling is a remnant of AD&D2, and probably a larger societal desire to shun labels in general. In the older iterations of the game, particularly AD&D2, the consequences of “alignment shift,” or really even how Alignment was viewed in-game, was left up to the discretion of the DM. The problem with that element, which I might add is not part of the current 5th edition D&D, is that it demands player character actions conform to how the Dungeon Master views your PC’s actions. The negative affects for an “Alignment Shift” appeared in one edition of the game and disappeared in the next; they realized that take on Alignment was flawed. In our present world, and in the world-building tools provided in 5e, the determination of what is good, evil, lawful, anarchic, or neutral is more subjective to the individual player, and they are given the ability to explore those options in the alignment mechanic. What was true in 1974 is still true in 2017, we are not dealing with only two options but the multiple gradations between good and evil as well as social order and anarchy. And if the society of your game world sees your PC as chaotic evil, but you feel in your soul that you’re chaotic good, we call that drama and the space for narrative exploration.
In general, I think a lot of people skip over delving into what Alignment is about because we believe that we already have a good sense for what it is. If you have not read the D&D5e’s statement on “Alignment in the Multiverse,” please do. It provides a wonderful rationale for why there are supposedly good and evil races in the D&D world.
For many thinking creatures, alignment is a moral choice. Humans, dwarves, elves, and other humanoid races can choose whether to follow the paths of good or evil, law or chaos. According to myth, the good-aligned gods who created these races gave them free will to choose their moral paths, knowing that good without free will is slavery.
The evil deities who created other races, though, made those races to serve them. Those races have strong inborn tendencies that match the nature of their gods. Most orcs share the violent, savage nature of the orc god, Gruumsh, and are thus inclined toward evil. Even if an orc chooses a good alignment, it struggles against its innate tendencies for its entire life. (Even half-orcs feel the lingering pull of the orc god’s influence.)
Alignment is an essential part of the nature of celestials and fiends. A devil does not choose to be lawful evil, and it doesn’t tend toward lawful evil, but rather it is lawful evil in its essence. If it somehow ceased to be lawful evil, it would cease to be a devil.
Most creatures that lack the capacity for rational thought do not have alignments-they are unaligned. Such a creature is incapable of making a moral or ethical choice and acts according to its bestial nature. Sharks are savage predators, for example, but they are not evil; they have no alignment. (D&D5e PHB 122)
So when we ask the question, why are there evil races, it is part of the cosmology of the D&D world. It is certainly within the purview of the DM and players to remove this characteristic of the world-it is your game after all-but then what system is used to replace the motivations of the 100s if not 1000s of entities the PCs encounter over the course of a campaign? 
People can always play a Murder Hobo if they want, but even that complete disregard for moral and societal structures fit within the Alignment system. True Neutral is defined by pure id. Though someone chooses to play a True Neutral PC doesn’t mean that character is incapable of performing acts of altruism, begin to show concern for others, or develop an undying hatred. It would take some other, major action in that PC’s life to make a shift from their fundamental outlook. Some may argue that is the reason it should be tossed, but a standard deviation is exactly what allows each PC and NPC to be unique. The freedom to role-play your character is aided by the Alignment mechanic; it provides his or her foundational drive.
I’ve used that term or idea a few times, ‘fundamental outlook,’ and I realize I should be clear about what I mean by that term because it is relevant to the idea of Alignment. When developing a character, we decide what makes that PC tick, his/her motivations, beliefs, past events influencing their present actions, belief in the gods or no belief. The summation of all those components are what I mean by ‘fundamental outlook.’ I call that Alignment, and Dungeons & Dragons call it Alignment, but if you want to call it something else like ‘character development;’ okay! There is still the core beliefs of the player character, those core beliefs can be changed because of in-game developments, and those new core beliefs will influence the choices you make for the character.
One of the more famous characters in modern fantasy literature is Drizzt Do’Urden, a dark elf. The Drow civilization are servants of the goddess, Lloth, and the Drow reflect her drive for power through deception. The race is known to be merciless and are feared and reviled by those living on the surface of Abeir-Toril. 
Drizzit’s origin story places him within one of the conniving, Drow clans, who are searching for any opportunity to move higher in the social ordering of Menzoberranzan, but he does not feel as if he belongs in this world. He can function and even thrive in such a world because of his gifts and talents, which becomes a test for him. Who does he see himself to be? Through the help of his mentor and father, Drizzit realizes the corrupting influence of his homeland and seeks to flee it. After many hardships he leaves the Underdark behind and finds the upper world unforgiving, and judges him solely on his race. It becomes another test for him: despair or perseverance. He proves him relentlessly as a Drow willing to sacrifice himself in order to protect those who cannot protect themselves, and yet he must travel to the ends of the world and live on the fringes of the outcasts. Drizzit’s undying faith in the good people of his world is undeserved. He finds help and comfort in his closest friends, who also have to overcome their own prejudices toward Drizzit’s race. They’ve come to judge people by their actions and not their prejudices. And with a resilience similar to Drizzit, they continue to champion their belief that judgment is based on merit and an individual’s honor.
The whole story of Drizzt Do’Urden, second son of the Eighth House of Menzoberranzan is predicated on conflicts between good and evil as well as civilization and nature. Hmmm, that sounds kinda familiar. But for the sake of subtlety: A-L-I-G-N-M-E-N-T! There are so many classic storytelling tropes in Drizzit’s life. The struggle between good and evil is palpable in the Dark Elf Trilogy. Drizzit possess a flame of good within himself that the oppressiveness of the evil within his society threatens to snuff out. Even if you don’t like the labels good and evil in this setting; fine, the struggle still remains between being himself and a larger societal drive to conform. Regardless of the name it is Drizzit’s internal struggle. He inherits this self-identity or goodness from his mentor/father, Zaknafein, who is a tragic figure. Zaknafein faced the same struggle as his son, but lost and took his place within Drow society. But Zaknafein had one ember of that identity remaining, which he bequeathed to Drizzit. As you read through the remainder of the Legend of Drizzit series, regardless of what order you read those books, you know there is something in his past that drives him to continue despite the prejudice, hatred, and thanklessness he receives. Drizzit is a Drow, who knows himself and his place in Faerun. He is forever pressed to the outer edges of society, willing to make hard decisions that others are not willing to make, and yet he desires to be of service to others and make the world a little better. I think the life of Drizzit and his companions, the internal and external struggles of identity, attempts to make changes in a broken world are stories worth exploring.
Alignment, developed characters, background, whatever you want to call it, are the engines driving the narrative of storytelling in RPGs.
I’ll be honest, I didn’t go watch the Cody Lewis video, so I don’t know what his argument was. But even reading your arguments, I still feel alignment, while sometimes a useful tool, also often gets in the way. I understand why you think PC Alignment is at times a useful tool, however I think the same utility could be achieved other ways without many of the downsides. In the end, I still feel alignment is a relic of previous editions, and it’s time we let it die so we can move on to something better.
You said “True Neutral is defined by pure id.” The official 5e definition is “Characters of [True Neutral] alignment don’t take sides in the battle of good and evil, and just do what they feel is best at the time.” But these statements, in my mind, are artificially limiting, and by limiting or excluding certain character concepts, are a hindrance.
For instance, I have a character right now who I label as True Neutral, worships a NE demigoddess, and really wants good to prevail. The thing is, he succumbs to the temptation of power, and this demigoddess has granted him a boon he can’t get elsewhere. He usually does good, even altruistic things, but he also sometimes (secretly) does evil, destructive things, purely to appease the evil deity who provides him his power.
He justifies this in his mind by telling himself he uses this power for good and so that makes it OK, but the truth is that at best he achieves a balance. He is not driven by purely id; he is driven by a desire to do good, by cravings for power, and by guilt and regret for the bad things he does. This is not instinct or emotion (perhaps the cravings for power are); this is a moral calculus. He doesn’t do what “feels best” in the moment; he feels regretful and guilty even as he chooses to do these evil, destructive things. He has been looking for a way to wean himself off this boon that demands evil, but he also worries about retribution from the demigoddess he worships, should he abandon worship of her. This is a fun character, and his moral dilemmas have driven some very interesting narrative, and yet even the 5e descriptions of Alignment directly contradict how I play this character.
As another example, let’s consider Tyler Durden from Fight Club. Is he Chaotic, Neutral, or Lawful? I argue he is Chaotic, because he wants to tear down the system. He’s willing to maim people and destroy things to achieve his goals. He’s not concerned with a replacement system he wants to build to replace the current system; his focus is simply to destroy, so that there’s room for something else to take its place. But others argue he is Lawful — just look at the regimented paramilitary group he formed! Others see those 2 things as achieving a balance, and label him as Neutral. This is another character who doesn’t fit well into the defined alignment system — how does a label of Chaotic, Neutral, or Lawful enhance this character? How would it encourage role-playing this character?
This brings me to perhaps my best, though subtle, argument for how alignment can impede roleplay and interesting narrative. You say “The summation of all those components are what I mean by ‘fundamental outlook.’ I call that Alignment”, but I disagree. Alignment is the LABEL you put on the summation of those components, and the act of labeling something changes how we think about it. An RPG can encourage development and definition of a character’s fundamental outlook without requiring players to assign one of nine labels to that outlook. As soon as you label, you create categories; when you create categories, you discourage things that bridge categories or fall into the cracks between them.
Furthermore, when you label, you discourage change. In general, D&D doesn’t encourage characters to grow, develop, and change over time with regard to personality and motivation — and labeling a character’s fundamental outlook with an alignment implicitly discourages it. Most “long” plots, such as a multi-season TV show, a series of novels, or sometimes even a single novel or movie, involve characters that change. But in D&D, that is subtly discouraged, which is a shame.
What if, instead, D&D required players to narratively describe a character’s fundamental outlook? 5e does do this through the Personality, Ideal, Bond, and Flaw statements in Background, but by making them explicitly tied to a character’s Background, that strongly implies they are set and unchangeable. So why not have another, more freeform statement which is the character’s “current outlook”, and is explicitly encouraged to change as the character develops? Would that not serve the same purpose as an alignment label, without many of the downsides? The same could be used for NPCs and races — why must we label Orcs as a typically Evil race, when we could just stick with the outlook description of “Most orcs share the violent, savage nature of the orc god, Gruumsh.”?
Couldn’t agree more. I also think that for new players, alignment provides a good introduction to thinking about how your character would act and behave when presented with various challenges. By choosing an alignment, it makes you think more deeply into who that character is. Which in turn helps the player roleplay that character and hopefully makes them a person as opposed to a murder hobo.