That's the only time it makes sense to run it.
The play is sort of a football unicorn -- I hope to see one someday, but I'm not counting on it. I have talked to several coaches about it so I know it's a possibility. I've heard of it happening in my neck of the woods only once in 25 years.
There's an added component that bears mentioning. This play is discussed among officials so much more often than it's ever seen that it's ridiculous, but if it ever is used, we'll have history.
Now consider this: If a down is replayed, all the rights and options available before the original play are still in effect.
Let's say there are 15 seconds left in a game and the white team, down by 1, forces a punt. The returner for the white team signals for a fair catch at his own 10 yard line and makes the catch (the second part is vital -- signalling and letting the ball go is not enough). Now there are 7 seconds left and 90 yards to go. The white team runs a play that breaks out but the ball carrier is tackled at the 50, however the tackler is flagged for a 15-yard facemask foul. Time expires during the play.
There will be one untimed down from the 35. However, even though the ball advanced 55 yards, because of the foul, technically the down is being replayed, so the white team still has the options available to it because of the fair catch. The white team puts the ball on a tee at the 35, The red team must back up behind the 25, no rush is allowed, and the kick will be to win the game.
So the real question is, if the white team wins, how many police officers will it take to quell the riot and protect the officials from the mob of people who will not believe that kick was perfectly legit within the rules?