Every villain has a reason.
Except Ozai, he was just an asshole.
Not really true.
Ozai you could argue has the purpose of Tradition, as he’s continuing a war that his nation has engaged in for several generations at this point, and from birth he has been indoctrinated into thinking that this is just the way things should be. He still goes a bit overboard for simple tradition, though, but you could also argue he is the villain of Moral Imperialism: he feels that he is the greatest and wants to conquer others to “share” that greatness with the less fortunate. There are ways Ozai can share in being symbolic, just not as clearly/strongly as the others.