Oh no, I have no doubt Aang loves Katara, and I have no doubt Katara loves Aang, but I don’t think that either of them are in love with each other. The love Katara shows Aang is almost always maternal, she’s a mother figure to him throughout the series, heck there’s even an episode where Aang himself acknowledges that she mothers him (tldr: oedipus complex, oedipus complex, oedipus complex).
Meanwhile, he sees a pretty girl who looks after him, and he mistakes that for romantic love. I feel like the most telling moment for Aang in that sense is during EIP when even after she says very emphatically that she’s confused and that it isn’t the right time, he kisses her anyway. He’s twelve and he has this idea that romantic love is simple, (“we kissed at the invasion and I thought we’d be together”) that any anxiety can be solved with a kiss.
I have no doubt that with time, Kataang would become a relationship I could stomach, certainly I love Tenzin and I think that perhaps when they were in their late teens to early twenties, Aang would have the emotional maturity to deal with that kind of relationship. But no matter how many muscles they piled onto him in the finale, he remains a twelve (maybe thirteen) year old boy, and he is immature. His love for Katara was selfish, possessive and childlike, because he is young.
All of the characters in Avatar had to grow up fast, but I think of all of them, Aang had the least of that. Katara virtually had to bring up Sokka, becoming the mother figure very young, and she projects that same mothering onto Aang. Sokka had to step up and be the warrior and hunter, Toph you could argue had an easier life, but her emotional maturity was beyond her years, she understands people and the way they work from a lifetime of observation. And really, do I even have to discuss Zuko? Aang had a childhood, at least initially, the first responsibility Aang had to shoulder, he ran away from, and the entire series is a coming of age process for him, he’s young, it’s both a virtue and a flaw in him. He is kind and compassionate and he gives a lot of himself, but he is also selfish in a way that only a twelve year old boy could be, (runs away from being the Avatar, won’t give up Katara for the sake of the Avatar state, expects Katara to love him after he kisses her with no other explanation, refuses to kill Ozai against the wishes of four Avatar reincarnations) which to me, indicates that he is not in love with Katara.
Certainly he loves her, and he might be in love with the idea of her, but the final kiss was the result of a badly timed, badly developed relationship that seemed slap dash and a quick fruition to all of Aang’s pining, but completely disregarded Katara’s own development and growth.
If it had to happen, I would have liked to see Kataang implied, maybe, just them standing on the balcony together would have been fine. I would have liked to see Aang recognising the issues with recovering from the war. I would have liked to see Katara returning to the South Pole to rebuild her village, or continuing her studying as a healer. I would have liked to see her personal development acknowledged, and not seen her reduced to a love interest in the finale.
Maybe Kataang was an inevitability, and I’m sure in a few years time, they would have been in a position to have a healthy relationship, but the time for it was not at the end of season three, for either character.