Spence,
What about the player that can't be beat because all the board cards are out and the cards are exposed before the final round of betting?
The original post, pre-flop, makes more sence for your argument. After the flop, turn, or river, I would rather rule no more betting. I honestly don't remember the last time I saw a dealer drop the deck stub during a deal but, I'm sure it's happened plenty of times.