One fact that gets VERY little attention is that expanding the playoff actually makes it LESS likely that a non Helmet (or at least near-helmet) team will win the NC.
Look at the BYU example. We all know that their NC was a ridiculous joke, but they have that trophy in their case. It took a lot of luck and a bunch of clueless poll voters, but it happened.
So, I think this kind of cuts to the crux of it.
The old system chase the undefeated-est team, which meant randomness abounds. Is relying on UCLA upsetting USC on the season's final week to swing a season that much different than a 13 upsetting a 4? Either one sacrifices some degree of finding "the best" for entertainment. Honestly, a tournament is more equitable because the ground rules are simpler. Win the games in front of you. CFB's old system couldn't even codify that.
And the idea of letting in the one small conference school isn't to make it more likely they'll win a title. It's to give them the ability to, even if that's just proof they never will. Sixteen seeds never beat one seeds, but there's a value in being there. There's a value in playing it out for everyone involved.
(OAM's 9-7 worries are interesting, but not all that actually concerning. In the NFL, the gap from the third-best team to the 13th best team is not unbelievably wide. In CFB, it very much is. And it's not like basketball, where the right two players and a hot shooting night can swing things. Football is wonky, and if anything, we've had the opposite problem)
Anyway, I don't know if a bigger playoff is the answer. I know the old system would likely be untenable in the modern landscape. But some of the concerns strike me as conflicting laments.