@oldfort You would be wrong on that. CBA for example already had 3 Princeton SCEA acceptances. The private schools you mentioned have about the same results but they cost 4 times as much. If you look stat for stat the boarding schools talk a good game but that is about it. There are plenty of parents that scratch their heads after spending $250k only to see their kid go to the same schools.
The only point you are right about is whether private school is necessary at all for NJ residents. The choice to go to Catholic school is more complicated.