If you had a son or daughter in such a school, how would you determine whether or not you're getting your money's worth?
I'm just posing the question as to whom (or what body) would judge whether or not educational standards are being met, and to what degree.
Second, how would people with low incomes fare in such an environment? Would they be able to afford a "Kia" education, while their neighbors across the tracks can buy a "Lexus" education?
In answer to your first question: by using my own years of education and experience to know whether or not the kid is learning math, English, history, science, etc. Teachers do not have a monopoly on knowledge - parents are very smart. The public makes excellent purchasing decisions already, and that's why we have the highest standard of living anywhere. The customers of the education business are themselves mature, educated adults, but right now they have limited ability to change public schools.
In answer to your second question: no system will ever result in "equal outcomes" (unless we are all slaves). The current public system certainly doesn't result in equal outcomes, nor should it. We have some public schools which are pretty good, most mediocre, and some horrible. We have those who go to the Ivy League and other expensive schools and those who can't afford it. That's the way capitalism works - everyone will not have a Mercedes.
Currently private schools offer scholarships and loans based on need, and I expect that will continue.
A certain percentage of parents don't care about their children's education, health, etc., and that unfortunately will continue.
AND some kids are smarter than others. They too will rise to the top. You cannot have equal outcomes -- too many variables in humans. And some kids just sit there like dumbheads.