Most teams want at least 7 home games a year. The Big XII and the Pac-12 both play 9 league games, The SEC will probably go to that format sooner or later. That leaves room for at most one home-and-home with a non-conference foe.
Bear in mind that Florida and FSU already have an annual non-conference game with each other; Stanford has an annual game with Notre Dame that neither side plans to give up.
Another issue is that many of those teams probably prefer variety to the same opponent over and over again. Everyone wants to get on Texas's schedule, so they don't need the certainty of a common opponent every year. Their future non-conference home-and-home opponents include USC, Maryland, Notre Dame, Ohio State, BYU, Cal, and Arkansas.
Oregon has scheduled similarly: their future home-and-homes include Wyoming, Texas A&M, Virginia, Michigan State, and Ohio State. If this happens at all, it's going to be in the 2020s, not right away.
Lastly, it's worth noting that most of these teams play in warm-weather climates, where a September game is going to put Michigan at a disadvantage. That, at the very least, is one issue they didn't have to deal with when playing Notre Dame.