Michigan doesn't help Utah win the PAC 12 South, either. Utah still has 2 OOC games to play, and now SOS matters. Many years, the B1G team Utah will play will be a patsie like Indiana or Northwestern. Instead of playing a Div. II squad, play BYU and get more national attention, keep a rivalry intact, and give yourself the best chance to make the playoffs under the SOS consideration.
"Improving National Stature" and "7 home games" are dichotomous. The 7th home game is a cupcake that won't help national image.