Your item 1) is suspect.
The rack-rate for private universities is exorbitant, but good students don’t pay rack-rate unless their parents are very well-heeled, and maybe not even then. Top private colleges and universities have very large endowments and can grant scholarships almost on a whim if they want to attract a particular student — I suppose some internal accounting moves some income from the endowment into the student’s account so it is distributed internally as tuition dollars are, though, money being fungible, I’m not even sure they always do that.
Our daughter went to a highly ranked private college on the East Coast, and we paid essentially the same as to send her to a state school here in Kansas. Why? She came out of HS with enough college credits that at a state school she’d have entered as a second semester sophomore with her language, freshman comp and math requirements fulfilled, had a 4.0 GPA, and came from Kansas (a plus for geographic diversity, since fancy private schools like to boast of having students from “all 50 states and N foreign countries” for some N > 10). They gave her fat scholarships and grants that brought the actual cost down to state school rates.
Hey, if the private college is cheaper than the public university, fine. Go for it.
All I know is that I come from a family of modest means, and private universities were out of the question for me. While I had reasonably good grades in most subjects, I was certainly not a straight A student and therefore I was not presented with any scholarship opportunities.