But I do believe that most University Presidents would rather be associated with Washington, Stanford, Cal (#5, #9, #32 in 2021 research expenditures) than with Cincinnati, Kansas, and UCF (#51, #72, #112).
Whether that's the right decision is an entirely different story. I'm not convinced that conference affiliation (driven mostly by football) makes a huge difference there. But I also exist in the world of academia and I know how other academics feel about it. And the University President is an academic in pretty much every case