Based on the riot at the last Charlottesville City Council meeting, I think they are all getting voted out for their poor handling of the protests anyway so it will be tough to tell the primary reason for them getting voted out.
In the UT case, the Regents have control over Fueves, right?
UT is a big can of worms that goes far far far beyond statues. The Kroll report came out a couple of years ago showing Powers (who Fenves succeeded) bought off support from the Legislature by admitting unqualified kids of elected officials into UT (which has very competitive admissions that just had an affirmative action case go up to the supreme court). The result is that UT is now horribly corrupt and mismanaged with massive administrstive waste and the house desperately needs to be cleaned for a lot bigger reasons than statues or liberal/conservative politics.
In short, UT's leadership has bought off key state support for awhile and feel free to do whatever they want with anything without caring what locals, alumni, students or the state thinks. If you want a reference for how out of hand it has gotten and what a corrupt scumbag Fenves is, see this thread:
https://www.hornfans.com/threads/ut-president-fenves-sued.104857/
Fenves ignored his own biased task forces he set up by removing all the statues and by overturning that sexual assault finding. In short, he is just doing what he personally wants to do.
Now the people could pressure the governor to appoint new regents, but they dont. In reality, almost all public education needs improvement at all levels, but people dont really care. Go look at the horribly low turnouts in local school board elections. Or they just vote for President and think Trump will just fix everything.
Anyway, UT has taken a financial hit. The percentage of UT and UT Law alumni that give is ridiculously low compared to other comparable schools (like laughably low). UT actually gets state oil money and unless the legislature cuts that off, UT probably can survive with 0 alumni giving. My personal opinion is that if UT continues to prioritize out of state students in admissions and continues to dump on the popular will of the people of the state, the Legislature should take UT's oil money away and use it to build better roads and infrastructure. Force UT to rely on donations like most schools and they would actually have to be responsive to alumni and locals. As long as they can buy off the Legislature with admissions, keep the oil money and do favors for a few rich daddies, King Fenves will continue to have total control over a state funded fiefdom.
Hopefully people will at some point start caring about public education at all levels and where there tax money is going. Right now, a lot of UT almuni are outraged about the statues and have stopped giving, but nothing will be done about statues or any of the much bigger problems if they do not put pressure on the legislature.
I think one of the issues is people incorrectly see UT as separate entity and do not understand it is a state institution funded by their tax dollars and their state-owned oil and they do have a say regardless of where they went to school or even if they did not.
The problem we have is, in a lot of these situations, is there is not very much responsiveness by leaders to their constituents and it is driving popularity for Trumps and Bernies.