I'm going to play devil's advocate and disagree with this point. While I'm sure tradition played a role in selecting Illinois, I'd be willing to bet that given the full range of options, Illinois is not in this bowl. USC has a guaranteed slot in this bowl. Without the whole "two team per conference" rule, you have three options:
USC vs. Mizzou (ineligible because OU and KU are in from the Big XII)
USC vs. Florida (ineligible because LSU and UGA are in from the SEC)
USC vs. Illinois
Personally, I think the USC-Florida game would be the game of choice because it would mean BIG money and BIG ratings for the Rose Bowl.
The right thing to do would be kick KU out of a BCS bowl since they don't have good wins or a tough schedule and shove Mizzou in that game.