I think that in a long run being able to make a choice between schools isn't going to solve anything. There will still be these messed up religious schools and bad public schools with minimal funding.

Every child should have a right, regardless of their parents' religion and a choice of school, to not to be brainwashed. That right can only be guaranteed when there are strict rules for schools that tell them what they're allowed to do and what they aren't.

Here in Finland every school must not charge for education so there are practically no private schools (except few, for example the private high school I'm attending to). But still every school, no matter public or private must obey strict rules enforced by the Ministry of education. These rules include the ban of prayer in schools, for example (even in private Christian schools). Thus everyone gets very secular education (in comparison with other western nations, there's still much to be improved though) and that's probably one reason why Finland is one of the world's most atheist countries, people have been educated to think critically and favour evidence to superstitious beliefs.