I think, and this is mine, that
...before the half, shenanigans like forcing punts at the last second result in more injuries and freak bad things (see below) than good things happening. And when you are a thin team with the cavalry not showing up until next fall, you don't risk injuries for low reward machinations.
...with 5 minutes to play, we had a higher probability of winning with a muffed punt than any other scenario, other than mind controlling Pitt so they forget that Ahmarean Brown exists.