So you want a megalomanic sociopath with a god complex and a tendency for pettiness to rule over a destroyed afterlife that needs a benevolent, competent and sane leader more than anything.

Aizen is a ruthless criminal who did countless atrocies, several just for shit and giggles, who also abandonned all reason and logic once he achieved transcendency and became close to god. We all say how Lille lost his shit after he became close to god, but Aizen wasn't much better. And that was when he only was close to god. How high will his ego rise, once he actually becomes one?

If Aizen became Soul King the world would have to bow to his whims. He would probably begin to create gigantic, compesating statues of himself and spent his day sending thunderbolts after Hinamori and Hitsugaya, while spying on little kids. His rule over Hueco Mundo wasn't that effective either.

Also I don't think a monster like him should allow to reach his goal end up as the ruler of everyone. That he dies is a more than fitting end.