@nobaka but on the other end it honestly looks like Saotome is literally their only source of town interest. If they don't really have anything else to parade around doing so would be tantamount to suicide. So while yes they LITERALLY have the power to do so. Politically they do not since she IS the town's image. Let's say that they do decide to pull their support because they're idiots (and quite frankly they have been shown to be). In the real world that would just leave Saotome to be poached by another town/school.
We know she's been on tv, she relatively famous as far as highschool athletes go, and she has done well so far in her career. If anyone got wind that she is up for grabs they'd shell out a decent amount of money to help transfer her to their school and become their star boxing player. Finally like you said, no one has been shown to be mustache twirling villains. Trying to parade someone to improve their town's image, yeah sure but evil not really.