I see it more the way Arizona has gone. The student is what's important here, not the school. The state pays the school to teach the student. Doesn't matter what school, private, charter, public, whatever. What matters is the school is effective in turning out educated graduates.
When you do that, and unions absolutely hate this, it means that teachers and schools have to be efficient and effective at producing results. That's what counts. If public schools turn out a shitty graduate, then they should wither on the vine and go under. If a private school does the same it should go under.
I am absolutely against public education and government having a monopoly on education, and that is exactly what the Left, teacher's unions, and the Democrats want. For them, it's all about the process, and the results are irrelevant.