Are private schools able to attract talented History and English teachers? It could just be the circles I go in but I'm under the impression that the reasons that people go into teaching those subjects are generally better aligned with teaching the public i.e. if you're teaching rich kids with engaged parents then you're optimizing diminishing returns while a little literacy can go a really long way in an underserved community.
Private schools often discount tuition for the children of their teachers, sometimes substantially. I knew more than a few teachers at my high school who taught until they got pregnant with their first child, quit until the youngest was in elementary, then went back to teaching - both to have something to do and to defray the cost of tuition.
And while the students and parents may not be perfect gems, they're a lot less likely to threaten actual physical harm.