Banning legacy admissions is a coordination problem. Try to eliminate it at one school and parents (re: donors) will raise an uproar. It would need to be eliminated at the whole cohort of peer schools to eliminate parents’ exit option.

Semi-related anecdote: my alma mater (Swarthmore) got huge pushback from donors when it tried to eliminate its football team, which was legendarily bad and created a huge, costly title IX imbalance (apparently football rosters can be 100+). So there was about as clear a case for elimination as you could hope for, and still it was a big controversy that hurt the school where administrators tend to notice — its endowment.

So when we talk about eliminating legacy admissions, I picture that, but just a thousand times worse.