Private schools that entirely lack unions (or protected tenure) actually have significantly lower teacher salaries than public schools, so your theory is incorr

Private schools that entirely lack unions (or protected tenure) actually have significantly lower teacher salaries than public schools, so your theory is incorrect. Add to that the fact that public schools in most states are terribly underfunded, and teacher salaries are pathetic across the board. Administrator salaries, on the other hand, are often way too high. A law (covering government-run public schools) that limited administrator salaries to 120% of the median teacher salary at that school would likely to more to raise teacher salaries than a union could, I think.