Utah might not be as popular a draw as BYU but that gap would close quickly with Pac-10 opponents filling the schedule.
The main issue (aside from the Sunday scheduling) would be the academic one. The presidents want high-profile research institutions, and Utah fits that mold and BYU does not. BYU is a great school for what it does aim to serve (undergraduates).
"Politically" there are some issues as well:
In 1992, the university drafted a new Statement on Academic Freedom,[70] specifying that limitations may be placed upon "expression with students or in public that: (1) contradicts or opposes, rather than analyzes or discusses, fundamental Church doctrine or policy; (2) deliberately attacks or derides the Church or its general leaders; or (3) violates the Honor Code because the expression is dishonest, illegal, unchaste, profane, or unduly disrespectful of others." These restrictions have caused some controversy as several professors have been disciplined according to the new rule. The American Association of University Professors has claimed that "infringements on academic freedom are distressingly common and that the climate for academic freedom is distressingly poor."
Stanford, Cal, UCLA, Washington, Oregon, and Arizona are all prominent members of the AAU, with Stanford being a founding member of that entity.