Private schools add literally no value to society. Study after study have shown absolutely no correlation between private schooling and eventual income/self reported happiness/career satisfaction/tertiary education success (after controlling for parental income and education level).
What private schools do is reduce social cohesion by segregating children by income and religion. Funny how conservatives are always in favoir of social cohesion when they are using it as a racist dog whistle but not where it actually matters.
I don't know if I'd go so far as banning private schools(some Montessori or Bush Schools etc may actually add value) but I certainly don't think these class exclusionary bohemoths should be getting any public grants or tax concessions.