reason (3) is social signaling.

elite schools aren't only desirable because they set you up with big opportunities. they are the way for high-school overachievers to signal to everybody how smart and good they are.

elite schools could probably make bank if they just sold a stamp-of-approval from their admissions committees that just said "you are smart enough to get admitted, but were not lucky enough to win the lottery of being given a seat".

100%, but it's even worse than that. "X got into Stanford" is the new "X is a Stanford graduate" because of grade dilution - and admissions dilution has soured even the former.