BYU focuses on undergraduate education (which I honestly laud them for) but that makes them less of a research school.

There are 29 public AAU schools at the FBS level. 28 of them (all except Buffalo) are P5. 5 of the 7 private AAU colleges at FBS level are P5 (Tulane and Rice ar G5).

Of the remaining 32 P5 schools, 27 of them (including Utah) are Tier 1 Research Universities. The only Tier 2 universities are SEC (Alabama, Auburn, Miss St), dragged into Big12 by association (Okla St, TCU, Baylor) or Wake Forest.

BYU is a Tier 2 research institution, which is a non-starter for the PAC12 or Big 10 and a very tough sell anywhere else.