>>108268529I'm not sure I can get behind this line of reasoning. We don't know if gender would be an issue when it comes to inheriting the throne. In fact, when Azula is about to be crowned, the Fire Sage named her Fire Lord, without any acknowledgment of gender whatsoever. Further, when Ozai is asking Azulon for the throne, he points out that he has two kids, both of them equally eligible to inherit and continue the line. Not much to go by, both to me it seems like the sex of an heir is largely irrelevant in the Fire Nation.
As for public opinions: the populace is generally cowed and reveres Ozai as a god. He doesn't need to justify himself to them in any way. The nobles and the generals most likely only care for titles and fiefs, so if they get that, they don't give a shit who sits on the throne.
The only reason I can see for these calisthenics in removing Zuko is that Ozai is such a raging narcissist that he can't even just come out and say "My tarded son is a tard, disowned", because it would make him look anything less than a perfect 10/10 genetic miracle who produces perfect children.