Why just public schools? At least in California (and I suspect elsewhere), teachers at private schools are paid quite a bit less than public school teachers.

I know this because I used to work at a private school! I did that for two years, then left all of it for a tech job so that I could climb out of student loan debt and actually have a decent life. (The basic issue is that parents can't afford to pay more because they pay twice for education: first they pay taxes to send other kids to school, and then they pay private school tuition on top of that for their own kids. The result is tens of thousands of dollars in lower pay for private school teachers.)

Anyway, the point of this isn't to dump on anyone's school. I just want to help correct the idea that private schools are somehow less worthy of care and attention than public schools are. The truth is that private schools are often in financially precarious circumstances!