I think BYU football in its current state is an accurate reflection of how the LDS church chooses to operate. I'm not saying that it should necessarily be that way, but I think there are more similarities than there are differences. For me to elaborate would require a change in topic from football to religion, and I've gotten into trouble with mods for going down that road before.
Basically, I don't see them making the kind of programmatic changes to the football program you and others are talking about, and I think that accurately reflects (rather than opposes) the way the LDS church and the BOT does business.