I've suggested this before, but once the TV bubble bursts, I'd argue that there's going to be a better incentive for power conference schools to go independent, at least for football. BYU's independence is kind of precursor to that. They've been able to schedule big non-con series with the likes of Wisconsin, USC, Washington, Texas, Florida State, and along with a slew of mid-level programs (UCLA, Mississippi State, Arizona, Washington State, Virginia).... They've had a few guarantee games but only with top programs (eg. with Nebraska and Michigan in 2015). Despite threats to do so, most of the MWC schools haven't blackballed them (they've played Hawaii, Utah State, UNLV, Boise State, and a few others), and they've only had a few series against MAC / CUSA / SunBelt programs.
With the recent news of the MWC likely adding Gonzaga, there's strong speculation that they would bring back BYU without football. If the MWC insisted they rejoin as a full-member, BYU would probably reject that, because they would become the top program in the WCC (Saint Mary's has been better in basketball of late, but that's not sustainable).
To some extent, New Mexico State (especially with rivals UTEP and UNM) and Massachusetts remain in FBS despite no prospects of joining a conference (and Liberty has moved up despite the same circumstances) because there are more than enough bowls to accommodate them, and they're able to fill their schedules with MAC / CUSA / SunBelt programs that they can beat if they're at all decent. Idaho moved back to FCS because the Big Sky is where they had more natural rivalries.
Back to my original point, if all the power conference schools were independents for football, most of the rivalries would remain (and some of the dead ones would surely return), and Michigan would schedule traditional Big Ten teams or more interesting opponents instead of Maryland and Rutgers. As for basketball and other sports, conferences still make sense, especially since the NCAA controls those post-seasons, though.