I don’t want to diminish your personal experience- but I don’t think your comment accurately describes most modern boarding schools.
Yes, there are super wealthy legacy types, and yes the schools rely on their money (some more than others). And yes, there are nutty entitled parents and students in all prep schools. Public schools too, btw.
My son is far from Richie Rich. We aren’t legacies anywhere or big donors. We have no connections. He has always felt supported at his boarding school, and so far in the college process there. So far their approach on college has been “let’s figure out what you want and what realistic targets are” and NOT “here are the leftovers, you are on your own” as you suggest. So I disagree with the assumption that boarding schools treat the abundance of “normal” kids who attend as second class citizens. It has not been our experience.
Like with @Happytimes2001 , One of the huge things he has gotten from boarding school is a deep appreciation for diversity (which he would never gotten at his public school), so much so that it is a major requirement for whatever college he will attend. I suspect the emphasis on diversity is new in the past 10-20 years, so perhaps after your personal experience. But it is real.
To your point, though, schools may vary wildly on how much they value and support all students, and that is worth sussing out. I just don’t agree that by definition these schools don’t support students who aren’t uber-wealthy. It sounds like the bs in question is one that has a good balance, and perhaps the day school not so much. I could be wrong.
I agree that the focus for OP’s decision should be the experiential difference between boarding v day school. I won’t repeat what was said above, which pretty much captures it. I would say, though, if the daughter was a fit for both, the money would sway me.