And their Round 1 opponent should have to win a Qualifier game to prove that they belong in the CFP field. At least a CCG participant has shown that they did well enough to qualify for an opportunity to play for a conference championship.
The other at large teams are, at best, the number three team in their conference and qualify via beauty pageant runner-up ribbon. Make the other at large teams earn their way in by at least beating another at large team on the field to qualify.