My thoughts on this.....
Why does it have to be one way or the other (conference champions vs. best teams)? There's an easy solution to this. Instead of a 4 team playoff, you make it a 6 team playoff.
You take the conference champions from the Pac 12, Big 10, Big 12 and SEC plus 2 wildcard teams. The top 2 rated teams get a bye and the other 4 play the games at the higher rated teams' home stadium. The winners of those two games get matched up against the Top 2 teams, with the games played at the home stadiums of the Top 2 teams. The final game would be played at a neutral site (could be rotated between different sites each year).
You always hear the mantra "the games need to be decided on the field, not in the polls or in the computers". If you don't take conference champions, where the games WERE decided on the field, how else do you decide the best 4 teams? Do you take sportswriters' word for it? Coaches who don't even watch the games? Computers? A selection committee that will always have built-in biases? To me, this is the fairest way. You reward conference champions (which should happen, otherwise, why even have conference games), plus give an opportunity to two other high-caliber teams who may have gotten upset in their conference championship game or maybe lost a game early on due to injuries or a fluke play, etc.