a missionary tool, they need to schedule 10 away games a year against big name school as one and dones, and lose. People admire and respect games against service academies because of what they stand for, they respect them, and they aren't beating the host schools.
I don't think byu football is a missionary tool, too be honest. I think it shines some light on the school and the church, but not enough for God to care and not enough for him to influence it, any more than he runs Mitt Romney's campaign or helped write the Book of Mormon musical. All those things bring light and discussion, but ultimately God still allows his children to lead them how they see fit.
I believe byu is lead by men of God who are trying to make the best possible decisions, which helps. But they can still make incorrect decisions and blow chances, just like all members