My kids won't consider BYU-I, because the NCAA sponsored sports programs make a difference to them socially and culturally. If they don't get accepted to BYU, then they will consider other options (USU, state schools) before BYU-I because being able to go to games, cheer on your school, whatever you want to call it, matters to them in the context of a complete college experience. Does it trump academics? No, but it's a part of the college experience that matters to them.
I'm not saying that BYU-I needs college athletics to be successful, but not having these things makes it different from BYU in more ways than just academically. And it's one thing that matters to kids like mine, so much so that Rexburg isn't an option for them. And it doesn't really have anything to do with them becoming bigger BYU fans.