Dave,
What happens when you count down the deck and realise that there are only 49 cards, or 50, or 53? Refund all bets...search the players...call security. Counting the deck is something that should be done after the hand is played out. Putting the "spotlight" on a holdout artist, or a "cheat" is not a good way to promote your cardroom.
What would YOU do if you found the deck had more or less than 52 cards? Play the hand out and simply put in a new deck for the next hand? Wouldn't the players want to know why they were playing with a fouled deck?
If there is an issue that would ultimately require you to unravel a hand, why wouldn't you want to stop action immediately to check if the issue exists?
"Spotlight a cheat"? Why wouldn't you? How does identifying a cheater and kicking them out of the room do anything other than make the other players more comfortable about playing there?
For the record, I deal, and act as TD, for a pub league. But we try to follow TDA/Casino rules as closely as possible.
Also, I have been at a cash table in a casino where a similar situation happened. After the hand was over, pot pushed and rake dropped, it was discovered that the cut card was in the shuffler - with a green light, and the card at the bottom of the stub was a card from the other deck. The floor called the hand dead due to a misdeal and unraveled the action, and returned the bets. Although I disagreed with the decision, I later learned that it was the correct thing to do.