Yeah I've wondered this from time to time myself. I suppose if the church is going to sponsor any sport for their members, it'd be one that could be done indoors, the space dedicated for it could be multifunctional, the sport itself would be inherently non-dangerous...
Football can and does easily lead to cracked heads and cracked knees and cracked ... well everyting. I'd love to see you try to fit a soccer field or a baseball diamond in a stake center. Now that I think of it, there really are not a whole lot of sports that can easily and always be done indoors. You might also notice most lds church buildings with a basketball court will also have holes in the floor for volleyball nets.
As far as promoting sports in general goes, I think it's awesome that the church gives us a place to exercise and stay fit in a fun and friendly environment. Well it wasn't that friendly for me when I was 14 but I suppose that goes without saying.... It was still fun
