The best case for a playoff system is made by the BCS itself. The BCS sucks!! When the BCS was first created it was supposed to put the two best teams in the country in a National Championship Game so that college footballs National Champion would be decided on the field. When it was created it was supposed to guarantee the following:
1.) The two best teams in the nation would play each other.
2.) No more split National Champions.
3.) No undefeated teams would be left out.
4.) Teams who play a weak schedule would not be able to make it based on strength of schedule.
No let's look at what has actually happened.
1.) The two best teams would play each other. Fact: this has only happened twice and one of those can actually be questioned. The first time was the overtime game involving Ohio State and the second was the game between USC and Texas. A case could be made that even though that was arguably one of the greatest games ever played many people forget that Auburn was undefeated that year as well. They were left out because USC and Texas styarted out ranked #1 and #2 and never lost.
2.) No More Split National Champions. This happened when LSU won the National Championship Game, but the AP writers voted USC as their National Champion. The AP has subsequently had their poll removed from the BCS rating system because it is so flawed.
3.) No Undefeated Teams Would Be Left Out. See #1. Auburn goes undefeated and doesn't make National Championship Game because they end up ranked #3 behind undefeated Texas and undefeated USC.
4.) Teams Who Play A Weak Schedule Would Not Make It Based On Strength Of Schedule. This actually worked to it's own detriment in< I believe it was 2003, when a USC team that was almost universally recognized as the best in the Nation was left out because Notre Dame lost their last game. This resulted in the split National Championship. There has also been the Nebraska team that got in (and was crushed) and the the last two years when Ohio State got in and were crushed. Is there any doubt that a game between 2 loss USC and 2 loss LSU would have been better than what we got last year?
The BCS system is irretrievably broken and solves nothing. A playoff system is the only option. I believe that an 8 or 10 team playoff using the current major bowls would sove this problem and make the bowls even more attractive than they already are because they would be directly involved in crowning the National Champion. The National Championship Game would, of course, be rotated among the major bowls just like it is now. The major bowl games would likely be much more competitive as well because you would, theoretically of course, have more closely matched teams in each game. No more Georgia crushing Hawaii in the Sugar Bowl or USC crushing Illinois in the Rose Bowl. The current system is so bad that it would almost be better to go back to the old one.