It's unquestionably the flagship public institution of the state, but it's not nearly as dominant within the state because a huge number of kids (and many of the state's most talented kids) are always going to prefer BYU instead.

The U must boil over watching the smartest kids in the state go to BYU, and see those BYU grads eventually going to Wall Street, to global law firms, to Big 4 accounting forms, starting major tech companies, etc. Most flagship public institutions enjoy the benefit of being the school of choice for most of the really qualified kids produced by the state, but Utah is always going to be fighting uphill on that. And it clearly eats at them.