If they moved up they would join a group of schools that used to compete for national championships and don't any more:
Arkansas State, Boise State, Bowling Green, Central Michigan, Georgia Southern, Louisiana-Monroe, Louisiana Tech, Marshall, Massachusetts, Northern Illinois, Ohio University, Southern Mississippi and Western Kentucky
All won either college division poll national championships, (1958-72), NCAA Division II championships (1973-77) or 1AA(FCS) championships (1978 to the present). None has ever won or played for the 1A(FBS) championship and likely never will.
Everybody should have a shot at winning a national championship. That's why divisions were set up. 1AA was designed for Division 1 schools that didn't have a real chance at a title- they could be Division 1 and get in a playoff for a championship. But many schools still preferred to be in 1A rather than 1AA for 'prestige' and so they could get a better chance at those "guarantee" games where they send their players to get killed by a major power with a huge stadium so they can get the money. Georgia Southern beating Bowling Green just isn't the same as winning a championship. I'd like 1A to be the Power 5 conferences and put the non-power five teams into FCS. That would give the Bison plenty of competition and it would look familiar to most of the 'demoted' teams because that's where most of them came from. D--1 schools could still play them but their kids would have a shot at a title.