Elite institutions with big endowments get so little of their operating budget from tuition that I don't think it's outrageous to expect one to break ranks eventually and go tuition-free.
Then I will happily give, and I expect a lot of deep pocketed alumni feel the same.
I believe Stanford University gets something like 40% of its annual budget from tuition (other top universities are similar). That's not huge, but it's big enough to make it totally infeasible to simply stop charging tuition.
For better or worse, these figures aren't quite as significant as they seem, because a lot of alumns restrict what their donations can be used for. E.g. the Widener one for Harvard's main library, which was fantastically restrictive even for that, and also required a swimming test since a son died in the Titanic disaster (not that being able to swim would have made much difference in water that cold).
So, yeah, the interest could pay for all the tuition, except X of it is restricted to the law school, Y to the med school, Z to arts and sciences but not in any way that it can contribute to tuition, etc.
Ah, and tuition money is particularly valued, because it's unrestricted....
It could, except that Harvard already uses a lot of the interest on that endowment to cover expenses. If they didn't have the endowment, tuition would have to be a lot higher.
Now would also seem to be a bad time, certainly MIT and Harvard are really hurting for operating and capital funding. Brand new Olin College (https://en.wikipedia.org/wiki/Franklin_W._Olin_College_of_En...) had to drop their full tuition offering to all students in 2009.
Tuition isn't really the issue. Most top schools have needs-blind admissions, so conditional on getting in, you will get funding if you need it.
Inequality stems from the fact that by the time they reach college admissions, students from richer families are already more qualified (at least in the eyes of admissions committees). Addressing this would require either changing the admissions process, or helping students from poorer families to become better qualified prior to the admissions process.
It's totally an issue. If you're a transfer student, you'll find that the few universities that go on about how proud they are to be need-blind and offer a great education to everyone!...now all consider need in admissions, or don't offer to meet your need even if you do get in.
Considering many low-income students start out at a community college, taking even one credit at one effectively locks you out from virtually all prestigious universities. It used to be the case that you COULD go from community college to a fancy private, but it's all but impossible these days.
Combine this with what you mentioned in the second part of your comment, and low-income kids are screwed both pre and post high school. It also screws over kids of all income ranges with highly dysfunctional/abusive families (who won't help with college, didn't support your pre-college academics/extracurriculars, won't sign your FAFSA, etc), since the only thing you can afford is a community college in those cases as well.
Then I will happily give, and I expect a lot of deep pocketed alumni feel the same.