I am actually agreeable to using conference championship games as a +1 of sorts, but I doubt we'd ever meet my requirements.
First off, the #1 reason you can't have this as a sole playoff criteria is because it can leave the #2 team out. This happened in the NCAA basketball tournament and they changed the criteria later on to avoid this. While it's not so bad to have the idea of a conference champ #1 vs. a conference champ #3 for a championship game, it is a bad idea if you start saying you're going to put in the 9th ranked team (or lower) but exclude the #2 ranked team.
Generally speaking, I understand the notion of not letting a team lose one game then play for a championship in the next one. OU did this and people went nuts. The problem was SoS, OU played more games (with more difficulty) then USC, so logically speaking OU with 1 loss still had proven more than USC with 1 loss. However, one of the major issues there was no Pac-10 championship game (and you see this theme in every controversial year).
If you whittled things down to 8 or less conferences (depending on size it could be as few as 4), AND every single conference had a championship game I would be open to the notion of using that as an elimination game. However, I would then want it to go back to BCS criteria. The top two teams to win conference championship games play for the championship. This might be a bit redundant, but by setting the criteria you'd basically be forcing everyone into doing this.