i think, with baseball, the situation is markedly different than football because of the 11.7 but not necessarily for the same reasons everyone is talking about. since the teams are limited to 11.7, private schools are at a huge disadvantage out of the gate. this probably balances out, to some respect, the benefits that many private schools have with their usually bigger endowments and bigger boosters.
we have a friend whose son was talking to a private school (D1, good mid major level baseball). at the last minute, a great in-state public school offered him and he accepted. all in, his dad said he was getting a pay raise (the kid goes to a private hs) bc with the offer, his tuition, books and room and board were going to be less than his hs tuition! with the private university, his hs tuition number would have been doubled.