1. Everyone likes to see big non-conference match ups. It excites the fan base and provides a good way to measure how good a team and conference really is. Conference teams scout each other so much that sometimes a really good team looks weaker in conference match ups.

2. Style of play. If you only play conference teams, over time specific styles of play will emerge that are really effective against your conference but can be exposed against other styles of play. Think BYU in the 80's, or preparing for the triple option or even building a team to face a Wisconsin offensive line or an SEC defensive line. You can become too specialized both in scheme and personnel.

3. You really do get tired of seeing the same teams and fans every year. Non-conference games are a breath of fresh air. BYU really needed a break from Wyoming, UNLV, New Mexico and the likes. Imagine knowing that all you have to look forward too is playing the same teams every year and hoping for an exciting bowl game matchup.

4. Already mentioned by other posters, but conferences having multiple 1 or 2 loss teams becomes much harder in conference only.

5. No 2 game warm ups against inferior teams to get ready for conference play

6. No more having 7 home games a year.