I've always thought that the NFL replay ought to be at the officials' initiative, not a coach's.
Designate a "Replay Official" up in the booth who decides whether or not to review a play, and then along with the referee and the one who called the penalty, whether it was a good call.
For the officials, such a plan would take away the negative of being challenged by a coach, and it would return the initiative of judging calls to the peer group of officials. In other words, a replay would become a sophisticated "conference on the field," instead the hyped-up melodrama it is now.