Someone wrote an pretty good write up on how a Zuko and Katara relationship would have affected the narrative:
I don't think I agree, given Zuko was essentially a deuteragonist. His importance in the story seemed atleast as important as Aang's. If Aang's presence made her a side character in his story, I don't think her getting with Zuko would have been significantly different. Personally, I always thought of Katara as a great feminist character because her complex characterization that is defined by her own agency. Her story was within Aang's, but that did not take away that she had her own journey. I suppose I agree that it would have subverted the trope of the hero getting the girl, but if you want to do that effectively, a more appropriate pairing would have been for Katara to get with some side/minor character instead of Zuko (like the way Zuko got with relatively minor character Mai, or Sokka with Suki and Yue)
That said, in light of Legend of Korra, I do wish that more light was shed on the accomplishments of the Gaang post-TLA. I mean, here's what we've got:
Aang who founded Republic City and was a figure of power as a politician in that time, Zuko was the Fire Lord for many years and is now leading the counter-attack on the Z-team's escape, Toph became the Police Chief, and Sokka a representative of the Souther Water Tribe who testified in Yakone's trial, while we have Katara, who by all accounts seems to fulfill the role of Gran-gran in the TLA series.
To me, these are sort of...weird. Okay, Aang creating a city where all four nations come together is appropriate for an avatar and a good response to the war that happened before. And Zuko working with him is just as appropriate. It is essentially what they set out to do together at the end of TLA. But the rest?
There's already been a bunch of talk over Toph and how her becoming Police Chief is an odd choice. I don't know if I agree, since I can definitely see a story where she ends up as that happening, but she could have just as easily become part of the military or maybe bending wrestler or whatever (that's essentially what she was as The Blind Bandit). Toph of TLA was a fighter, and I don't see her living her life happily if she can't do that, so Police Chief, while somewhat odd, is appropriate. But then Sokka became a representative of the Water Tribe? A politician, really? The TLA series kind of painted Sokka as a renaissance man of sorts. He was a warrior, he was a military tactician, he could do haiku's on the spot, he was a swordsman, he invented blimps, he was good with mechanics, he was an artist (not a good one, but he clearly kept up the practice regardless of talent). So, while I definitely see why the Southern Water Tribe might need a representative and he may look as a good pick because of his journey with Aang, it's odd that they have him end up a politician of all things. He should have been the Leonardo da Vinci of his time (though..you know, probably not as talented).
Which brings us back to Katara. See, while I might find the position that Toph and Sokka took to be questionable, what is going on with Katara? Every other character here has some official position of power, but with Katara, it's more implied. They clearly respect her word on things, but I'm not sure if she has any actual power, and I don't know what she's exactly done besides raise a family with Aang. I feel her being the representative of the SWT would be more appropriate than Sokka, since she was the more culturally concious and concerned of the two anyway. She was the one that was always trying to learn more about and preserve her culture and family (it's what got her into the whole mess with Hama). It'd make sense that she'd be the one who would bring the SWT back into the world, but it doesn't give us any indication that that happened. Back in Book 1, I had assumed that Katara was the one who lead the legislation against Bloodbending (which would make sense, given her history), but it never actually said that either.
So, while I'm happy with Katara from a feminist perspective in TLA, LoK has her essentially just been "The Avatar's Wife" and not much else if we are going to go by what the show said.