I have kids. The reason I bring it up with an “If I were emperor” qualifier, is that for an individual, it doesn’t make sense to keep your child in a failing public school if you can afford to pull them out. It would take a unified effort of banning all private education, for it to actually improve things. I’m aware it’s a pipe dream right now, and as long as private schools exist, it still makes sense for individuals to use them.
It’s similar to the tragedy of the commons… people acting in their own self-interests (better education for my child) create a situation that is worse than if we had a collective strategy (we all get a decent education, and get to share a better, more educated society.)