Yeah I don't like that idea.
How about instead, that if a team loses any significant time to an official's error (and really this is only at the end of the game or end of the half or in the last two minutes...): The Head Coach can toss a challenge flag. Allow a team to challenge an official's error based solely on time; whether that is 3 seconds or 10 seconds or whatever...
That way a team is not penalized (loss of down? no way!) except for losing a timeout if a challenge is lost. Now, challenge flag rules apply, one per half and a TO must be available... OR, each team is given one special challenge per game reserved only for official's errors that impact game time. That way other challenges/ timeouts are not affected. No one's going to save a timeout just in case an official makes an error at the end of the game that kills the clock...
I would want a special Official's Error Challenge Flag, one per each team, one per game, that challenges only the time lost due to official's error...
Not going to happen but.. that's the way I'd approach it...