Desi,
If you go by the rules that currently exist for tournaments, then I would say that the dealer should not turn the cards over. I don't want to keep repeating what I've already written. I think that Rule #9 needs some rewording because it contradicts the order of showdown when there are multiple players in the hand and one or more players are all in. It's perfect for head to head when a player is all in and there is no more betting. That is what we are talking about. The example that you give about the action being on the river is perfect, and in my opinion, is such a regular occurrance that most of the time players "let that rule slide," so we can get on with the next hand. You are also correct when you mention how it could slow down a game. I think the issue here is when someone complains that a player intentionally attempts to muck a hand when they shouldn't. Remember, if the player turned their hand over the way they are supposed to, we would not be having this discussion. I think we would accept a rule that would make the dealer the responsible person to table the called hand.
Chet and Thomas,
If the rules that I listed above are not enough, I have more. THE PROFESSIONAL POKER DEALER'S HANDBOOK:
Under Sequence of events; (in part) Dealers, read any hand as soon as it's shown, but do not attempt to read a hand until the player turns up all his cards, and never turn up any players cards on your own. Another section under Dealer Information: "One player to a hand rule" dictates that they should be turned up by that player. Anyone other than the hand's owner who turns up a card is helping that player to play his hand. It's bad enough when another player does this, but it's unforgivable if the dealer does it.
Desi, There is a specific order of showdown and it is generally accepted when a player that has a strong hand announces his hand before he has to. The rule is for players that want to see the opponents hand first, and neither player wants to show their hand. This is when the dealer will ask the player that initiated the last bet or raise to show down first. If the round was checked, in a flop game, first to show is the first player clockwise to the button. In stud, it's the high hand, except in razz, then it's the low hand.