This scenario played out exactly for a good friend of my kiddo.
Father is in STEM and mother is a stay-at-home mom. I am guessing that the father is making good money (I believe he has an advance degree from S) and most likely the family will not qualify for financial aid at elite schools. The kid is very smart and hard working. Father made it clear that he was only willing to break the bank for H and P knowing that the kid can get into our various state schools (they are quite good) for sure.
The kid got waitlisted at the ivies and ended up at our flagship state school with Regent scholarship. Last I heard, she was doing very well there.
I think if you are upper-middle class, you really need to consider whether paying $65K a year for a private college is prudent. YMMV