The church has its share of serious issues. I know BYU athletics have their own issues as well, but they are still an emotional tie to my time at BYU. I'm working to square myself with the myriad of issues with the church from historical problems, to conflicting and shifting doctrines, to current social issues. I'm not sure these are issues that I'll ever be able to fully come to grips with. The one unflinching connection I still have to my ward, and thus, the church, is BYU athletics. I know I may be just one person, or one person among a very small minority, but it would really, really be difficult for me (RM, former Branch President, former member of 3 bishoprics, former member of a stake presidency, among other assignments) to continue on if BYU athletics are cut off.
I don't know your definition of missionary tools, but to me, BYU athletics continues to be a missionary tool.