A.ang ending up with Katara renders the entire show kind of meaningless
Strong words, but I've thought a lot about it. And I think A.ang ending up with Katara undermines any deeper meaning there could have been to A.ang's journey and story of ATLA on three separate fronts: it undermines A.ang's role as the last Airbender, it undermines his role as the Avatar, and it undermines the arcs of most of the other characters.
He fails at being the last Airbender
So first of all: Others have pointed out the hypocrisy of A.ang holding to Air Nomad teachings so tightly that he was willing to let the world burn rather than kill Ozai, and then turning around and violating them (specifically the apparent celibacy of monks and lack of traditional marriages or families in their culture) to be with Katara. I don't have a ton new to add there.
Aside from bringing it up way too late in the game, I don't hate the angle of A.ang taking Air Nomad teachings as seriously as possible. He's the only one left who can live them out. That could have been a really good story beat.
It's such a bad look, though, that he was willing to let the world burn for his values...but throws them to the side so he can get laid. The girl he has a crush on lives in the world!!! Saving the world is more important than getting the girl, and if you actually care about the girl she kind of needs a world to live in. If you're gonna violate your beliefs it should be with killing Ozai and not getting Katara!
To put a finer point on it, he's not a stone cold killer by nature, but he does have a crush on Katara. When his beliefs say "Don't kill" he has no problem sticking to them (he didn't want to kill anyone anyways), but when his beliefs tell him something he doesn't want to hear, like "you need live like a monk if you're gonna be a monk, so let go of your attachment to that girl", he ignores them and does what he wants.
So...in the end he only follows Air Nomad teachings when they align with what he wants to do anyways, which means he's not following Air Nomad teachings at all, he's following his own selfish desires. Him ending up with Katara renders his position as the last airbender, the last person alive who can truly live as a genuine Air Nomad monk in accordance with their beliefs and teachings, ultimately meaningless because his actions make it apparent that he doesn't actually take that role seriously.
He fails at being the Avatar
This one is more subtle so stick with me.
I know someone in real life who will defend kata.ang with the refrain of "But A.ang had to have kids!" and I always think, "But did he?"
I didn't watch much of LOK but I know there's some hand-wavey stuff that happens to bring back airbending en masse so in the end it renders his repopulation efforts kind of moot, but I'm not talking about that.
There's this early Christian heresy called Pelagianism. The details aren't important but the relevant gist of it is they believed that although the supernatural exists, there was no need for divine grace or supernatural intervention. Humans can just white-knuckle our way to perfection. You can do it alllll on your own through sheer willpower.
So I'm kind of going to accuse A.ang of pseudo-Pelagianism here.
The world of ATLA is one where the spirits are very active and present, and supernatural intervention is a regular occurrence. I don't think we're supposed to read it as a lucky break that A.ang got safely frozen away right before Sozin's Comet's first pass, and woke up in time to avert disaster with its second pass. I think that's supposed to be divine intervention at work in the story.
The grand finale of the story even hinges on this point: A.ang has disappeared, they go find Iroh to try and figure out another way to fix the problem of who will take on Ozai, and Iroh tells them to do as they planned anyways and trust that destiny is on their side. The fate of the world is at stake, and it essentially all works out because they have a little faith. They don't try to white-knuckle their way through fixing every problem via purely material means and purely human agency.
And while it could have been way better written to not be such a random eleventh-hour surprise, I do like that it's the divine intervention of the lion turtle and A.ang doing something mystical that only the Avatar can do that ultimately saves the day. I think that works great! It makes a lot of sense in the context of the worldbuilding and the storytelling, it's actually a very fitting resolution.
And the Avatar, of all people, is supposed to be the bridge between the spirit world and the earthly plane. Surely, when faced with a seemingly insurmountable crisis like the end of the airbenders and the breaking of the Avatar cycle, the Avatar will find some similarly fitting solution with the aid of the spirits...oh...oh no, the only way we can solve this problem is through purely material means and human agency, by having kids.
The thing is, attacking a problem with earthly, non-supernatural solutions is how Sokka would solve it, not A.ang. A.ang should solve Avatar-level problems in a way that only the Avatar can, if him being the Avatar actually matters in this world.
The Avatar should have been solving this problem with some cool soul journey and spirit shenanigans and inner growth or something. I personally think his new ability to energy bend should have given him the power to not only take away, but to give bending to people. That would have been a great solution that flows naturally from the plot.
The fact that he supposedly has to solve it like a scientist in charge of repopulating a nearly extinct species instead of like a powerful spiritual figure violates the worldbuilding in general and undermines the role of A.ang as the Avatar specifically.
And he renders everyone else's story meaningless
At the end of season 2, A.ang's crush on Katara is presented as an attachment he needs to let go of in order to master the Avatar state and end the war. Cool--that makes his crush on her actually relevant to the plot instead of an unimportant side story, it sets up a classic wants vs. needs conflict that the hero has to face down to save the world, it was almost great writing.
And it sets A.ang firmly on the same path as so many other characters in the story. You see the same basic character arc play out over and over in ATLA: character has an attachment, a fixation, an obsession that is causing them to make self-destructive and harmful choices in pursuit of their goal. They either need to learn to let go of their attachment, or it will destroy them.
Iroh is, in a way, destroyed by his fixation on conquering Ba Sing Se. Zhao is destroyed by his fixation on killing the moon spirit. Jet and Hama are destroyed by their fixation on getting revenge on the Fire Nation. Ozai is destroyed by his fixation on ruling the world. Azula is destroyed by her pursuit of power and perfection. That professor from Ba Sing Se University is destroyed by his obsession with Wan Shi Tong's library. The cabbage guy is destroyed by his attachment to his cabbages?
I think Zuko is the only character who lets go of his unhealthy attachment to finding the Avatar/being the perfect crown prince/winning his father's love and approval before it destroys him and he comes out the other side a more self-actualized, healthy person who ends up getting rewarded with everything he was fighting for in the end and then some (i.e. he becomes friends with the Avatar, becomes Fire Lord, accepts that his father's love and approval isn't something he could or should ever have to try and win, and that Iroh was more of a father to him the whole time). Which means Zuko's the only character that actually, like, completes the central arc of the story successfully.
And then there's A.ang. The main character, the center of the story, the guy in the narrative that all the other side stories ultimately serve. The show's named after him! Surely his reckoning with this repeated thematic arc in the story will crown off the whole damn narrative.
(We all know the answer here).
In the end, A.ang never actually lets go of Katara...he makes no sacrifice, he does not confront the conflict between want and need within himself, he does not overcome his attachment, he holds on to that fixation with both hands until the bitter end...and it doesn't destroy him. The solutions to his problems get handed to him in the form of a magic rock and a lion turtle. He does nothing to achieve self-actualization or growth or meaningful change, he learns no hard-won lessons, and he still gets rewarded with the object of his attachment.
So...in the end, what was the point of watching all those other characters learn the same lesson over and over and over and over and over again about letting go of your attachment before it destroys you? Especially if, the most important time this arc plays out, the capstone message is actually, "Well, sometimes you were right all along to cling to that attachment and you'll get rewarded for it instead of destroyed?"
Anyway, that's why I think the final shot of the show renders everything in it ultimately pointless, and why everything post-canon has been kind of unsatisfying...lacking that spark, that je ne sais quois that made so much of ATLA great.
At first glance the show seems like such great fertile ground for so many good future stories to spring from, but that last shot of Katara and A.ang kissing really salted the earth in so many different ways.
