And so that wouldn't happen, the Avatar is in charge of balance right? Just because a nation get concured doesn't mean their way of life dies with the country, new leadership really doesn't mean much a unified world WOULD bring about peace, what's the point of fighting over land if it already belongs to everyone?
The Air Nomads (why are they called nomads if they have temples?) are pretty much passefists a world with no war? Not that bad of an idea.
Earth Benders would give them the most trouble and resistance, they're rock heads, stubborn and would refuse to change for anyone. But if you pretty much just let them govern themselves then it should be okay, Ozai might have been going for that kinda thing. But with a Firebender as the leader.
Water would also oppose this system too but from where they are living its not like they has a say in it anyways, hello people no one wants to visit!
Strickly speaking though if the fic was more about a "what if" the Avatars were supposed to be the supreme rulers of the world? Think about that, the last Avatar Aang was supposed to rule the world but maybe Roku wasn't as nice as he could have been and people were pretty burned by him - get it "burned" by him? ahhh right- Sozen did the world a great favor by getting rid of the Avatar at the time using the Comet to strengthen his powers enough to fight Roku and win.
Then when the next Avatar learned who he was (Aang) he fled because he found out that they were coming for him the next day. Sure it could have been a misunderstanding but maybe not and he ran away.
Well a Hundred years later the Avatar hasn't shown up for a very long time but without a strong leader to guide the people and keep them unified (weather they want to be or not) In fighting has started. ALL of the nations are enemies to each other though the Air Benders have managed to stay neutral.
Think about how THAT story would go.