@surelyhuman is correct that the UChicago board is entirely self-perpetuating. They can change that at any time, I suppose. Not sure that the alumnae network has the infrastructure to “vet” candidates “appropriately.” Boards don’t want mavericks - they want “team players.” That’s true for all of them. So, as @JHS indicated, the candidates aren’t likely to be the types mentioned in that Yale article I linked above. It’d be great if they were, but they aren’t likely to be.
But even if the board were sufficiently open-minded to hear out a maverick, the vote-on coalition is very small on any university board. The large majority of the trustee positions at the Harvards and Yales and Princetons remain appointed. Stanford’s alum rep. is an appointment of candidates vetted and suggested by the alumnae association. So the appointeds still wield the main decision-making.
Finally, this might be true for all great universities, but being appointed a trustee comes with a price. I believe that UChicago has a smaller board by at least a few positions than some of these other places. Unless they increased the number of spots to allow vote-ons, pretty much every one of those 49 spots (other than the president’s) means dollars lost for the university.
Larry Summers - interesting example to bring up. There’s actually a back story there and anyone is welcome to look it up. Here’s the Crimson’s account: https://www.thecrimson.com/article/2006/2/10/tawdry-shleifer-affair-stokes-faculty-anger/ From what I’ve heard (all 2nd hand, of course), the board hated Summer’s guts over this. The university paid damages and they might have lost a couple of significant benefactors. So Summers’ politically incorrect comment was just the catalyst needed to remove him. BTW, Schleifer was on faculty at UChicago for a bit before moving East 