I agree strike-3...I've worked in both private and public settings. The successful public school coaches work their butts off for chump change just like the most successful private schools. The things I have seen that are advantagous for the private school is the parental and alumni support. The few "well to do" parents at the public schools do all they can and rarely do you see a strong alumni group...at the private school "MOST"...not all...the parents are "well to do" and do all they can to support the program.
The public coach tends to do the things that the more numerous private parents do (fund raise, field work, team meals).
I agree that the enrollment numbers have nothing to do with the competitive level of a team...it is the # of kids that are willing to play the game. Success is the #1 recruiter...private or public