This would seem promising.

People could then decide based on the merit/reputation of a school, in the way they decide post-secondary. It could re-align incentives to being performance-/interest-based and create healthy competition to attract more students. Certain schools would probably exhibit more conservative and some a more progressive bent, but it wouldn't matter because you could choose. Low-enrolling schools would have to close. Enterprising people could open a school if they thought they could make a go at it! I think you'd still face many of the same issues we see in colleges, but it would be an improvement.

I'd have to look more into what Malice has to say about the violence, but I think kids being around others who are like-minded might help on that count too.