> Of course it would be ideal if those born into privilege also could clear the SAT.

They often do. Or at least are very close.

I got into an elite engineering school (off the waitlist at the last minute, no donation/legacy), and the admission folks basically told me "we accept the top X, but if we just ignored the top X and took the next (X+1)-2X (or three), the result would be the same."

Basically, these schools are so competitive that if you wiggle things a tiny bit, on the margin, you're not really sacrificing much. However, if they wiggle too much, that would obviously degrade pretty quickly. But from my experience, that hasn't been the case.

So a school like Stanford is probably thinking, within the margin of noise, if we let in folks because their parents did well here as students/faculty/etc, that's probably net positive.

The donor one is a bit different, but again, on the margin, and with some math around donations vs Cal Grant, they probably see it nets out better for them.

Admissions has a tricky job since there are many more outstanding students than they have slots for - even limiting to perfect test scores and grades (usually with top quality essays, recommendations, etc. as well.) Many applicants end up with the same admission ranking (and those rankings still have a large margin of error as you note). Selection becomes arbitrary, based on ancillary factors (hmm, how many concert pianists vs. cellists are we admitting? do we have too many prospective CS majors and too few history majors?) Which is why they argue that at the margin they can consider demographics (for example balancing the number of men and women), geographic origin, socioeconomic status, athletics, donor status, etc. Truly random would be fairer however.

The problem has worsened over decades; applications have ballooned ~7x (600% increase) since the 1970s, while class size has only increased by 15%.