College football playoffs

It has recently been a hot topic with many college football fans: should the bcs switch to a playoff system? I personally would love to see it changed to some type of playoff system. The current way the bcs does things, a lot of teams are left out of contention even if they have done everything they could to be considered the best in the nation.
These past few years have left many people questioning the system in place. This past year Utah went undefeated, won thier bowl game against what was, for a majority of the season, the number 1 team. Also a few years back Boise State went undefeated and also won their bowl game. Its teams like that, who go undefeated throughout the whole season and win their bowl game that don't get a chance to prove that they are the best in the nation.
I know that some people make the argument that teams like Utah and Boise State don't play the type of caliber teams that others play and that their conference is weak. But with wins in the bowl games against powerhourse teams, why can't they get shots at national championships? They have proved that they can beat the "better" teams and stick with them.
If college football switched to a playoff system it could fix all of these problems. I know that some people argue that the current system makes the whole season count and not just the end. But if it was switched to a 12 team playoff system it could fix that. With 12 teams, four of the teams would get a first round bye, this makes it so that the regular season games do matter and that the best teams get to make it to the second round automatically. The remaining eight teams play it all the way through. This would make it so that even the teams that are from "weaker" conferences but are still undefeated get a chance to become the national champions.