Maybe the problem is that going to an elite school matters too much for arbitrary social reasons. We've all heard and read about how hiring at places, such as elite financial institutions, will simply discard any application from a person who didn't go to an elite university. No one wants to lose out on opportunity.
Why can't elite universities increase enrollment to increase the number of opportunities? They have the endowments for it. I'm not aware of any Ivy struggling to pay its bills.
If society thinks that people who attend these schools are a better value, then wouldn't it be of benefit to try to expand capacity?
It seems like an artificially created scarcity. Do top schools feel their brand is diminished if they start accepting 2k students vs 1.5k?