This would completely erode any public perception of prestige of any University that implements it.
Suppose that instead the auction was only open to people who got put on the wait list after the regular admissions process?
Top schools get a lot more qualified applicants than they have openings for, and a lot of people end up on the wait list who are just as qualified as people who were admitted.
https://google.com/search?q=harvard+legacy
Other private schools are no different.