As far as money goes, coaching pay doesn't come out of money collected from pay to play. Coaches are under contract with the school district and schools are not supposed to pay for coaching contracts with money collected by students paying fees.
I don't think kids are charged per game either. I think it is a fee to cover costs of uniforms, travel, umpires, field maint., etc.
Not a school finance expert, but as a school employee, I do know there is a 'law' or 'rule' about school money and coaches. Boosters are not allowed to pay for assistant coaches anymore either.
Northmont's fees are pretty reasonable, and with three kids playing a total of 6 sports, it is nice to get a break financially. We spend quite a bit of money going to basketball and football games during the school year. Personally, I think it stinks I have to pay to watch my kid play ball.