But on the other hand, I don't approve at all of public humiliation as a punishment, even in milder forms. To me that's an abuse of power that is on the same spectrum as bullying.

Sorry, but I could not disagree with you more. The use of power is inherently coercive. This is the situation in real life: there are some people who respond to nothing less than force. This is a very minor use of it. Public humiliation for bullying, using a social punishment for a social transgression, makes the punishment fit the crime. It involves no physical punishment. And I believe it would deter escalation, because unlike an adult, the student has to go back and face his or her same classmates afterwards.

And the "same spectrum" argument never holds any water by itself, I think, because almost everything called bad by anyone is a matter of degree, which in a different intensity is not widely controversial.