Yes I know, BYU Hawaii and ricks College, etc. etc.
But if BYU were to withdraw from competition completely, it sends a horrific message. In order to remain unspotted from the world, we are going to wall ourselves off and disengage? We may as well declare ourselves the Amish of the Rockies at that point.
Shutting down the athletic programs renders us a whole new level of weird. Prominent and visible members and BYU alums would criticize the move and many may say seeya later to The Church altogether.
Could sports drop down a division? Flounder in permanent mediocrity? I think both of those things could happen. But shutting down the athletic programs at BYU? The backlash would be costly. I'd expect even the least enthusiastic about sports at the BYU BOT know this.