you are correct, these kids do not "need to go to private schools." But, usually they are better off. My point, is it's a lower risk, It's a lower gamble to go there- they have a much better track record than every local public school- I'm talking about the "best" kids, Power 4. I'm not sure what you mean that the Peter's kid was "recruited more" than the Central kids is just not true. I'm not a Central booster, or alum, i dont "love them" but they put more kids in big schools, it's really no debate.
In many ways, public/local is better, especially for the "average" or even the "good athletes," which is why i am talking about the 1%, the best kids. Private schools have less rules, more flexibility, which makes it easier for college recuiting. It is very diffcult to build and maintain a successful public school football program in western PA- that is why there are so few of them. Butler, Woodland Hills, Gateway, Lebo, North Hills, even USC- these are schools that "used to be great" and really are no longer- this is why they "lose kids" to transferring. This happens due to shaky coaching, or shaky resources, or a combination.
And again, the "payoff" is now real money, as soon as they graduate high school.