Based on the previous reporting regarding playoff expansion, ND not being in a conference would relegate it to being no better than the 5-seed in every playoff, regardless of record, meaning it would need 4 wins to be champion. Yes, there may be greater access to the playoff via more teams, but telling your players, hey, we value our independence so much, we are going to force you to win an extra game in the playoff regardless of how well you played in the regular season sure sounds like a shitty deal to me.
At best, playoff expansion is a mixed bag for ND. Considering the rest of college football has abandoned tradition, I would prefer ND do the same, stop being stubborn and join a conference to gain the possibility of those bye weeks. With USC now in the Big Ten, it seems like a no-brainer at this point.