Private schools get to attract kids from public schools and take away the talent. You look at schools like Blanche Ely, Boyd Anderson and Dillard for example. It's no reason why these schools aren't competing at a high level. Just drive through these neighborhoods during football season and every little league park is standing room only. Could you imagine American Heritage, Cardinal Gibbons, Chaminade-Madonna and St. Thomas without those 5 star players. This is just Broward County though.
Now when it comes to Dade County private schools don't run anything which is why schools like Booker T. Washington, Carol City, Central, Homestead, Norland, Northwestern, Palmetto and Southridge are pretty good year in and out. Except for Columbus no other private school is doing anything.