My son's school is paid for by the parents, and the teachers make a lot more than $10,000. Probably less than at public schools, but not much less. Plus, I still pay for everyone else's kids' school, too.
Here in NJ our private schools (religious or otherwise) are closing because nobody can pay $7K+ for the public school system in taxes and on top of that pay a private school tuition. One of my wife’s friends went from making $15K teaching in a private school to $33K in a public school in the course of a year; only a well-off person could afford to teach in a private school.
Without vouchers that would allow parents to use their education tax money for private education, most of those schools will be closed within a few short years. The teachers’ unions have successfully prevented vouchers from being implemented, and as long as they are the de facto owners of the Democratic Party that won’t change.