catch the BYU Mission and purpose vision. Not just sports.
I have been in wards outside Utah, where BYU coming to town (dance team, Choir group, other non-sport activities) was a big deal. Sports teams coming is also a huge deal.
BUT
I agree to some degree with the OP. We could do more. I would love for BYU (maybe the CC) to help send BYU gear to members in other parts of the world. I heard about one guy who send his missionary son a box of BYU Tshirts to give out to members where he was serving (I think it was in Asia somewhere).

Anyway... I think the majority of Active Church members are anxious to Support BYU, be it sports, or other activities, but we could also improve and do a better job, making it easier for them to show their support.