Using your logic, if you live in Utah you should like University of Utah and Utah State because they are the state of Utah's universities. It just doesn't work that way. I was in a meeting with a couple of members of the quorum of the twelve presiding and one of them,(it's been long enough ago that I can't remember which one) stated "BYU is not the Lord's university, the Temple is the Lord's university." I see BYU sports more of a tool for BYU students and alum than for the church membership as a whole.