They did this like 15 years ago, and had the clock run when the ball was kicked, and continue running after the special teams play, it was stupid and they got rid of it after a year.
I think Bielema gamed it one time.
I would get rid of any automatic reviews, and go to a 100% challenge system. You get it right, good on you, you get it wrong, you lose a time out. If you are out of timeouts, you cant challenge anything.
I would also be fine with the clock not stopping on first downs anymore