Well, one way the story could get there even with a Zuko more similar to the MC is to have him be motivated by 'go back to the palace with the luxe and the sexy chicks who'd be more than happy to get on with the prince that it imply' rather than 'recover my honor and earn my father's love and respect', same action, different objectif, just like the MC basicaly does like Aang by learning all four element, he just does it for very different reason.
Remember that Zuko in the show was basicaly stranded at sea on a boat with only dudes around when we first see him, if we assume he was more similar to the MC, he'd be just as motivated to capture the avatar if not more, the only place that would really pose probleme would be Kyoshi Island, since it's full of girls but as the fire nation prince, he had 0 chance to be welcome anyway and maybe he also had a weird Tsundere vibe toward Azula in their version, given how Azula has a yandere vibe in book 2, that would make Zuko jump ship with Azula at ba sing se just like in canon.
I mean, i see how you could have trouble picturing it but it can work IMO.