I taught for a few years, and I met many parents and students. The old adage is right: judge the tree by its fruit. Voucher-funded charter schools don't even have to cherry-pick students to surpass public schools: the biggest factor is that parents have to make a conscious decision to send a child to a charter school over the default public school. The worst-performing students belong to parents who will not put in the effort to choose a school instead of sending their kids to the default public school. There is a direct correlation between the parents' (or more likely parent's or grandmother's) lack of involvement in the child's education on the child's performance in school. The easiest filter to separate the bottom of the population from the average and top is to provide a choice of schools, because the lowest segments simply will not make any choice.

Fair enough, but my impression of lots of public schools is that they are abysmal and the few that aren’t are typically only available to rich people anyway (in practice, not principle) so the current system addresses neither overall quality of education nor inequality.

That’s the ultimate issue though. If parents don’t have the choice then we never really know that.

Right now, the only parents with a choice are the ones who can afford all the options, including moving to a better public school district.

But isn't it a good thing where birds of feather flock together? Just not being dragged down from low scoring kids is worth it. Why can't they select for criteria they are looking for?