If everyone except Kronk knows Principal Amzy is really Yzma why isn't she fired?
Perhaps she has tenure?
Knowing what Yzma is like, it's possible that everyone's just humoring her. After all, she doesn't seem to realize that everyone already knows. Plus she's not a bad principal either.
Perhaps Kuzco has yet to be liked to that point. Yzma's plan involving fake aliens invoked the fury of some peasants who stated that, while they don't care if Yzma dethrones Kuzco, they're upset that her plans harmed them.
If Kuzco was dethroned and forced to attend school, then who is running the kingdom?
One small issue: In "Yzmopolis", Yzma declares that Malina should walk the streets in shame because she's beautiful and smart. Now obviously this a jab at the fact that Yzma is neither of those things, but this is where the whole thing turns reaches a dead end; Yzma is neither beautiful nor particularly intelligent, but she does perceive herself that way. Why would she order those qualities to be shamed instead of admired? And more importantly, why do it to Malina of all people?