I will say that first, I Skar's second explanation makes a lot more sense than the first. (I too was going to post that the football department doesn't get tithing money.)
I can see his point, in a way. In my mind, the football department/team would be a wonderful way for BYU and the church to place values in front of fame. If they made a point of using only LDS players who were valiant in their testimonies, they could show this off as the way we think things should be done. We'd lose more games, but we'd win a moral victory. (By the way, this goes for the cheerleaders and their uniforms too.)
However, I will point out that most college football programs are vital to a school's money flow. Football generally pays for all of the other sports--without the revenue its tickets bring in, other programs wouldn't be able to function. The football program is actually an appeasement of the alumni, many of whom really want it, and who are willing to donate large sums of money to the university because of the loyalty a team brings. In addition, the notoriety the team gains the school cannot be discounted.