Good!
Let education be paid for by grants and the student own income, most grants. Plus force the universities to make their tuition cost effective.
Edit: However many years ago, public universities charged a fairly nominal tuition and survived for many doing that (financed by their respective US states). These public universities today have massively expanded their costs, primarily based on capital spending and follow the model of private universities.
While I attended college, tuition costs almost doubled, but since haven't increased much per year. It wasn't massive increased spending, it was the state cutting off basically all finding. There's certainly fat to be cut, but the admin costs are mostly imposed on high.
Some enterprising law students figuring out they could get a loan to learn how to get out of the loan - and end up with a very valuable degree out of it that could not be repossessed - and by the time they needed good credit, it would be off their records.
It took awhile for word to get out, and then they banned getting out of student loans.
So blame the lawyer (students) I guess?
I know people who would GLADLY throw away two years of their life in bankruptcy proceedings if it means they could be free of their crushing student debt.
Harvard in particular is so wealthy it always charges tuition based on ability to pay. The poor who go to Harvard pay nothing. But, of course, the poor seldom go to Harvard because they aren't admitted.
Just saying. There are mid-range school where, all else being equal, your scenario might be true. But those school depend on those same lower income students and, well, I'd be in favor of them buckling and charging less.
Also there are lots and lots of programs state and private to fund low income higher Ed. It is not a dichotomy.
If underprivileged kids represent anything above about 5% at Ivy's I would be shocked. One stat from Boston Globe was that only 3% of Harvard comes from the US bottom 20% economically.
The Ivys do more to perpetuate the existing power dynamic than they do to raise anyone up. They are far too small and far too nepotistic to do otherwise.
If you want to raise the middle/bottom up, you need to look at the large state university systems which are orders of magnitude larger.