You are not alone. There are many parents who feel this way about their college-bound kid. What does your son think? The typical boarding school structure and rules for students will be very different than the relative freedom of a freshman in college. That might be OK for some kids, and, for others, it could be suffocating (especially if they’re in close contact with high school peers who are already partying away at college!)
The vast majority of PGs at the top boarding schools are athletic recruits. Many have college offers in hand and are attending a boarding school to get their academic chops in place before diving into college academics and athletics (alternatively, particularly with boys, taking an additional year to grow and mature physically). Some have D3 offers but are holding out for an elusive D1 scholarship. Your student would need to be an impact player on the varsity team to be considered.
Consider in what significant way can your student enhance the boarding school community. Maybe there are arts and music PGs, I don’t know of any. A friend’s kid was a PG at a top boarding school and when meeting a new student at school and mentioning that they were a PG, the response was always “What sport?”.
If you’re not aiming for the typical elite boarding schools most mentioned on here, then there may be more opportunities, and some schools would welcome an additional full pay student! Call them and ask (although as a parent of a student who could soon attend college, it’s probably better if your son calls, not mom!)