According to Jack Swarbrick (Notre Dame AD who helped draft the 12 team recommended CFP expansion)

"I do think it’s helpful to us to say, ‘Look, Alabama put its position at risk in its title game or Oklahoma put its position at risk in its conference title game. We’re doing the same thing in the first round,'" Swarbrick said. "We are on par in that regard other than enjoying a potential 1-4 seed.”

So basically they wouldn't have to play a conf championship but they wouldn't ever get a bye and he thinks that is a fair trade-off