If a school is failing, parents simply won't send their kids there. If they do, it's their choice.
If they don't like something about a school, they don't have to go there. They can choose another.
For example; Christian schools don't have to allow Sodomites. That's their religious views. If sodomites don't like it, they can go to the public schools they've created or open their own. . It's a choice.
Look at homeschools. Parents, who are not accredited, are kicking the public schools butt! Accredation is an NEA thing. They invented that, not the parents. Actually, nonaccreditated parents are doing a better job.
Secondly, do you really think that private schools will be able to withstand suits brought by teachers who believe there has been discrimination in hiring practices at a govenment funded (and, therefore, no longer) private school?
And, how will private schools be able to maintain private school admissions standards? Won't they be "discriminating" if they don't take a student with "special needs" or with a "disciplinary record"?
And, if, as is the case in Florida, the students are required to take the state "assessment," who really controls the curriculum?