> From quit rates, to pay, to conditions, and beyond, but ignores the obvious which is that private pay and private conditions are largely pinned to be just above public salaries and conditions

Most of the private schools around here pay a lot worse than the public schools, especially if you factor in total comp w/ benefits. We have a tiny number with high enough tuition that they might pay well (but I wouldn't count on it), but almost none of the rest do, the bulk of which are Catholic or protestant religious schools.