@Bastion2.0 , you do present a very hard position to counter with this one. But that's what I enjoy about our discussions: you force me to think things through in a civilized manner.
I think that you do a great job of summarizing the biggest impediments to Zuko's early reign:
His former status as a traitor and terrorist.
The extreme degree of indoctrination that his people have been subject to for at least five or six entire entire generations.
The very radicalized reforms he intended to implement.
The stark change in the status quo.
These are all extremely valid points. And Zuko was known to struggle immensely during the first year of his reign, as evidenced in The Promise Trilogy. He even had to have his room relocated in the palace to ensure his safety due to the multiple assassination attempts.
Ukano's New Ozai/Safe Nation Society was a pretty obvious example of the holdouts who remained loyal to the previous regime. And the fact that Mai's dad was also a nobleman who lost his political power to Zuko's regime when he refused to follow up on Zuko's reforms and edicts would motivate just about anyone in his position into starting some sort of rebellion.
But I have to reiterate one of my original points: because Zuko legitimately claimed the throne and through a means that is in line with the then-current national identity and traditions of his country, Zuko would most likely be seen as the rightful ruler by a considerable portion of his people.
And the fact that Azula banished nearly all of her staff, advisors, and most likely a fair number of her generals, I can't imagine that many of them would feel much loyalty to the old regime due to the fact that their previous ruler left such a demonstrably unstable heir in charge while he lead a scorched earth campaign across the sea. They would more likely to follow Zuko than Azula due to the fact that he's not an unstable, paranoid lunatic who would be very likely to strip them of everything the minute they disagreed with her.
Zuko's reforms and change in the direction of his nation may have been counter to the 100+ years of a more imperialistic culture, but Zuko would be far more likely to incentivize their cooperation through negotiation or promotion than Azula, who would have either banished or incinerated any dissenters. And while he did strip Ukano of his governorship, he did not imprison, banish, or physically harm the man. Zuko is more than capable of standing his ground politically, but he is not incapable of compromise. After all, he did not strip Ukano of anything but his leadership position. Ukano still came from a rich noble family. Zuko was fine with allowing the man to keep his accumulated resources and did not press the man further until the conclusion of Smoke and Shadow. This is a move that I imagine he replicated several times over. It's far easier to keep a nation stable by slowly shifting the status quo with a few conditions attached. And considering the direction he was taking the Fire Nation, I'm guessing that many of the higher ups were counting themselves lucky that he wasn't more punitive in his responses to resistance to his reign.
And Zuko's fight for the right to have the oldest colonies in the Earth Kingdom remain would have been seen as a commitment to his people and earned him considerable loyalty from the public.
Mind you, Zuko's reforms never reached their intended conclusion for the entirety of his nation.
As far as the culture of imperialism and ruthless social climbing was concerned, we did get to see that in Ashes of the Academy. And we also got to see how rough it was for Zuko to get his educational and cultural reforms through. Hiring his ex to work as a teacher and agent of his on the inside was easily one of Zuko's smartest moves politically. After all, Mai knew firsthand from her time at the same school and from her experiences with Azula how toxic the culture of imperialism was. And while slow to get going, we got to see how effective she was at the change in direction. As with the case of the headmistress, Shihan, we saw how damaging the previous regime was even to those who taught it. Mai citing Azula as the natural conclusion of that system was enough to wake up the repressed headmistress and turn her against her predecessor and de facto foster mother.
The dark and destructive legacy of Azula and her brief reign over the Capitol would have been a pretty drastic motivator to get people to follow Zuko.
I'm not saying that any of this would have been easy. And honestly, I agree with you wholeheartedly that a bit more of a look at the difficulties faced by Zuko in the early days of his reign would have helped to support the idea of him being able to largely successfully transition his nation away from their warmongering past. Hopefully we'll get to see some of that when the new movie hits theaters early next year.
It's a damn shame we saw nothing of the Fire Nation in The Legend of Korra. It would have been fascinating to see the Fire Nation 70+ years post-war.