The reality is, some private schools actively recruit (and scholarship) athletes. Years ago, when Porter-Gaud proactively sought to enhance the diversity of its student-body, it took the opportunity to recruit student-athletes into the fold. Pinewood also aggressively recruits and supports student-athletes.
It's a tad more complex at the Catholic schools, such as B.E. But please, PLEASE, don't portray the Bishops as Simon Pure. Their coaches are ALWAYS on the lookout, and word is that soccer players are "encouraged" to play their club soccer for DISA.
My solution for those who don't like the public/private crossover is simple: Either legislate a more equitable enrollment/affiliation formula, or get your local public school to improve its level of play.