Even if the few hundred non-Mormons were ousted from BYU, they’d be tens of thousands of slots short.
And this discrepancy grows when considering graduate programs… BYU can’t provide graduate education (and shouldn’t—it’s limiting and looks incestuous) to every LDS student who wants to remain in Utah.
It makes sense to grease the skids and keep lines of communication open with local schools, and donating a few million here or there is a great way to make sure that things stay friendly. As anti as you think Utah is, I guarantee it could be a lot worse—and would be a lot worse—if the church actively gave them the cold shoulder.
How much is the church giving Utah anyway? Aside from the one-off gift here or there for a new building, I’m not aware of the church funneling much money Utah’s way.