Utah gains absolutely nothing by playing BYU. Nothing.
Utah is bigger and better than BYU. It's that simple. If Utah were to somehow lose to BYU, fans would freak out and demand that Whit get fired for it.
Also, as a side benefit, it really separates the recruiting in Utah. Most "championship caliber" athletes in Utah have a choice to either play for a team that plays USC, Oregon, Stanford, Michigan, etc or a team that plays Idaho, New Mexico State, etc. Who would you rather play for?