Thefan78: Your title "They don't have to recruit" is only half right. There are kids/parents who want to go to catholic/private schools. I have no problem with getting a great education. As a whole, the catholic church encourages priests to recruit kids to go to their local catholic schools. My sister-in-law is one of those who did (Prendie). But I don't think this is what you're referring to.
Do catholic school coaches recruit? Absolutely. No different than the priests. It's how the catholic schools survive and stay open. Football: back in the early 2000's, I coached in the Bert Bell league. Public school coaches weren't permitted to attend games (violations), but catholic school coaches could. This all happened before/ during/after the catholic schools joined the PIAA.
Public schools: I completely agree with what you're saying as far as the politics and underachieving coaches. But there are coaches who have a steady winning records in upper and lower classes. In the lower classes it doesn't matter if you're a great public school coach or not, if you don't have the bodies, you're going to struggle. The upper classes have more bodies to choice from. So, there are a few coaches/schools out there that are the exception. As far as kids leaving, common on, that's a loaded statement. How about people moving out due to economic reasons, health, work transfers, parents have girls not boys, concussion issues, etc. Many factors go into community evolution.