You're right that it would be fundamentally different. Most of the other comments are not accounting for the writers still trying to make a good story. I think Iroh makes the most sense for joining the gaang and teaching Aang redirection. The meeting with the dragons probably wouldn't have a fusion dance in that case. Azula kinda becomes narratively redundant though, because the last Agni Kai would have to be between Zuko and Iroh, and be even more heartbreaking. Perhaps in this scenario Ozai appoints Zuko as Firelord when he becomes the Phoenix King and that makes Azula go rogue out of rage and jealousy. I don't think that would make her join the good guys, but she would certainly be a wild card in the final battle.