At first it seems kinda of stupid, an emperor forced to go to school in order to retain his Incan emperor headdress.... And then I realized: maybe the entire show was an attempt to keep kids in school. Hm....
That is a good point. Part of sending Kuzco to school is to make him relatable to a young audience who know what it's like.
Kuzcos' Aesop Amnesia makes a lot more sense when you remember that he was spoiled his whole life before then, so it would take a while to get over that.
Kuzco's immaturity struck me as odd even as a kid. Then I realized, he's not younger than he was in the movie; he's just able to act his real age. Spoiled or not, as an Emperor from a very young age (If not a few months old when his father died) even with a regent, and being spoiled, he was still expected to act a certain way.
Concerning the ending of the series, it seems odd and unorthodox that Kuzco merely bestows Yzma a lowly job as Kronk's secretary as punishment. But it's also fitting for at least three reasons. First and foremost, she can't really be pinned down for her crimes of trying to usurp the throne: she has a secret identity, Principal Amzy. Second, in "Evil and Eviler", it's proven that deep down, even Yzma isn't entirely heartless herself. So Kuzco is showing relative lenience towards her. Third and finally, Kronk has been nothing but dutiful (even if it was to do her dirty work), and Kuzco's just giving him his reward for being such a hard worker.