The LDS Church heavily subsidizing BYU Athletics (think Nike and Oregon) would be extremely counterproductive to the missionary work of the church.

So then the argument becomes...well we should subsidize, just not enough to create a bad PR situation. And the LDS church kind of already does

A portion of all tuition at BYU goes to support BYU athletics. It's hard to find data since 2019, but looking at 2019 and the years before that, each year BYU got about $10M allocated from tuition. Which is not directly paid by the church. But it is paid by students in their tuition...with that same tuition being reduced by tithing money. So it's an indirect shot, but absolutely the same impact as the church taking that money to support BYU athletics