BYU is good at those sports because Mormon (I know we aren't supposed to use that word anymore) kids want to go to a Mormon university so they can date and hopefully get married. Their parents brainwash them from birth that they have to go to BYU. And guess what? There are tons of very athletically gifted Mormon kids out there. So BYU essentially collects all these kids in random sports without having to really out-recruit anyone.

But basketball and football are different because people do care and top LDS athletes are willing to give up the BYU experience to go play for a national power.