Azula's trademark Firebending represents her pursuit of perfection and her sadistic nature. Ozai is apparently the epitomy of what Azula craves to be. Now if this was true, Ozai's Firebending should of been blue, however this is not the case. The Blue part of the flame is hotter than the Red, Yellow, or Orange part of the flame, so why didn't Ozai use Blue fire in his duel against Aang? That's rhetorical, he couldn't use Blue fire because he sucks.
Ozai couldn't conquer Ba Sing Se through military force or deceipt. He could of gone there himself as a tourist and used make up. He doesn't have any distinct look to him, if they would notice him, then they should of noticed Azula and Iroh as well. Iroh, at least, has more military expertise, and has traveled the World more, you would figure that Iroh would be identified easily when he came into Ba Sing Se.
Iroh would of succeeded in conquering Ba Sing Se if his son didn't die. If Ozai was the most powerful Firebender of all time, he should of helped Iroh by bringing in more soldiers with him and continue to led the war effort when Iroh was mourning for Lu Ten, and conquer Ba Se, THEN take the throne from Iroh, but instead he was begging for the throne like a clever cow......ard.
So there you go:
Azula's blue fire represents her mastery in Firebending and her cruelty and Ozai is the epitomy of all that is cruel and his "more powerful in the art of Firebending" than Azula and still cannot create Blue fire, which is the hottest type of fire there is.
He didn't use Blue fire in his duel against Aang, and if he chose to, then he is stupid
If he is considered the most powerful Firebender because he is in great shape and isn't young and inexperienced and isn't frail or old then imagine how powerful Azula would be when she got to his age.
Azula should still be alive <3 and make an appearance because she is perfect.