If catholic schools paid teachers the median regional salary, 2/3 of them would have to close inside of 6 months. The money simply isn't there. It's really nice to say "teachers have a huge role, they should get top pay." But like every other utopian "oughtta be" statement, reality bites hard. There's no magic sugar daddy to make it happen.
As a catholic school parent, I get enraged every time my property tax bill comes around and I shell out another $5,000 to the local public school district. This utterly corrupt body (U46 in Illinois) spends somewhere in the ballpark of $12,000 per student per year and gets consistently poor test results. And no wonder when they cram 30 students per class, teachers have no real disciplinary powers, and waste humungous resources on non-mission critical agendas and politically connected staff and consultants.
In spite of the fact that EVERYBODY would win if public school districts awarded private school parents with a (say) $1,000 refund for each student at the end of the year, nobody will do it. They'd have MORE money per remaining student to squander as they see fit, but still won't do it (private school enrollment would grow enormously under such a program). That says to me that they care more about power and control than getting Americans educated to the highest degree possible.
In my area, an average public 6th grade teacher makes around $65,000 a year (before extra income from coaching, summer school, etc). If my catholic school paid their teachers that I simply couldn't afford it, my tuition would go up by at least 65%. We already drive old cars that I keep together with bailing wire and duct tape and not a few prayers, what more do you WANT from me??
Want someone to be angry with? Send your ire straight at the NEA. They want you (private schools/teachers) exterminated and are doing their best to do so.