A modest proposal: ban donating to them so they need to radically increase their student body (online or offline) to earn their keep with tuition, instead of relying on the donations of the extremely rich parents of legacy admissions students.
I'm mainly thinking of elite institutions. I'd first invert the question and ask what problem places like Harvard, Yale, MIT are currently solving. (This small set of elite universities is absorbing the vast majority of donations.)
As the number of student has exploded over the decades around them they've kept their student numbers the same as before even as they collect more and more money which they hoard with no concern for opportunity-cost-of-capital whatsoever. This has created an intensifying zero-sum battle for the admissions slots in these universities. Meanwhile the state systems are increasingly overwhelmed and sketchy private universities are increasingly scamming students on the edges.
By keeping their numbers so low, the Ivy League retains comfortably small classes, no major change in their overall mission and professorial lifestyle. At the student level they function to perpetuate privilege across the generations, especially via legacy admissions which seems like a gilded age concept I can hardly believe is still a thing in 2020.
I'm saying if the Ivy League were to change its mission to serve America and the world as much as they could instead, it would do a great deal to help the vast mass of striving students who are barely not making the cut, as well as the economy over the long run, and even reduce tensions in American democracy. And that change of mission probably can only happen if they start to ignore what their biggest donors think they should focus on.
I'm in an online Master's program now. With way more students than I feel they can handle. I'm sure they're milking the tuition just fine, but when projects and papers aren't graded in time to determine if you should withdraw or soldier on, it's less awesome.
While your view makes sense in the theoretical, once again human failings cause it to not work well in reality.