I don't think that would be a good idea. It would introduce an admin burden on the schools related to moderating/monitoring the sites. And they would more than likely overstep in one way or another, when enforcing their rules.
But sure, yeah, there'd be some admin time spent managing it. As with anything, there are plenty of reasons not to do it. It struck me as a low cost-to-impact ratio thing that could get kids into tech, but reasonable minds could disagree.
It would result in rampant wildness and people complaining, but if you didn't do it that way the burden would be too high.