The for profit ones mainly target students who couldn’t get into public universities. The elite ones target students who use public universities as backup. I think some of those students (particularly non wealthy students) will switch to making the elite universities the backup, contingent on the financial aid package. And I think that will have atleast some effect on administrative budgets. The elite universities maybe non profit, but in practice they are run more like hedge funds.
It students are willing to pay $20k more / year for private and public cost goes down by 20k, the private ones will be less competitive unless they also reduce their tuition proportionately. No ?
I doubt competition will hurt the private ones that much. They already have orders of magnitude more qualified applicants than they can accept, and are making very difficult decisions to turn a lot of them away whom they'd love to have.
The losers here would not be the elite private institutions, which will always have high demand and did even 50 years ago when public higher education was sufficiently subsidized that almost anyone could afford it with a summer job.
(Many of those institutions are already offering free tuition to lower and middle income students anyway. And they’re all incorporated as nonprofit entities.)
The losers would be the low quality for-profit degree mills that advertise on the subway and radio and charge students ridiculous tuition for degrees that won’t help them get ahead.