Teloch asked: NEW IDEA SCENARIO! No war, Aang never got frozen, Zuko eventually becomes the Avatar. And yes, still Zucest.
Azula would still be a prodigy, and if Zuko was already bitter that she was outshining him in everything despite being younger, he will feel even worse once he finds out he the fucking Avatar and she is still better than him. However, he'd be treated much, much, much better by the people around him, which would make Azula bitter since she's used to being the golden child AND because she's being ignored because of how great her brother is supposed to be in the future, while she is already great. They're going to be fighting A LOT.
However, once Zuko starts to making progress into becoming a firebending master, Azula can't help but grow to respect him a lot more - which only gets even stronger when despite of everything, he is still humble enough to recognize that he still needs help and that she is the best option. By the time he is a master, they're actually getting along really well.
Unfortunately, Zuko would then have to travel around the world to learn to control the other elements. They try to convince people that he can just learn at home, but it's no use. So, they settle by having Zuko come back to visit as frequently as possible and Azula going to meet him as well.
Every time they have to split up again, they get more and more upset, and at first they don't really understand why. But then people start making plans to find proper matches for both of them, and the reality of how they feel for each other comes crashing down on them. The second they are reunited yet again, Zuko proposes to her, and neither of them will EVER allow anyone else to try and separate them. They get married just a few days after Zuko comes back home for good.