Banning private schools is an extreme position, but I see some sense in it. Here's how I think about it.

It tends to be the wealthier, better connected, more influential people who send their kids to private schools. So, we have a situation where the influential people don't have a lot to lose if public schools happen to be under-funded (their kids get private education). So it is more politically tolerable than it should be to under-fund public schools.