The best team could also be someone that has one loss. Only a sensible playoff can determine the real champion.
It could also subject the best team to an unfortunate loss in the first round due to injuries, having a bad day, etc. Just as the one loss team in your scenario might have suffered the same thing 9 weeks earlier.
I'm not advocating for or against here, but I do think that the value of a playoff in football isn't the given many of its champions would think. The winner of the basketball tourny isn't always arguably the best team going. How many times have serious contenders suffered an upset? How many contenders have had their road made easier by others being upset? Surely in football the folks at (insert BCS conference here) will scream and howl the moment they lose to a CUSA rep in the first round. "Unfair seeding!"
It's kind of like the MVP debates: Is that award for the best player, who may be surrounded by great talent, or the one who meant the most to his team, even if that team didn't do so well? There've been planty of times where the team that was clearly the best throughout the season wasn't able to finish the deal in a playoff. Thus I feel we'd have almost as much debate about the validity of a national championship no matter how its decided.
Just for consideration...