I'm not saying that it should be done every single time. That's ridiculous and predictable. However, you mustn't forget...
"The players are not Sherlock Holmes."
I never said
the players were Sherlock Holmes.
If the players come up with a great idea, why not let it work?
But we aren't talking about a great idea. To remove the blush from the pig, in point of fact in cases like this the players are just plain wrong. This isn't like me saying, "No." They are free to chase the red herring however they like. I'm not quashing reasonable choice here.
If you limit the solutions to the mystery, I find that it equally limits 'skillful play' on the part of the players.
??? I'm not sure what you mean here. I'm using 'skillful play' in the Gygaxian sense of someone who well, begins to avoid having all the failings listed by Justin Alexander. They do thoroughly research. They find clues and figure out there significance. They don't latch on to conclusions immediately, but create several tentative theories that they keep and mind and refine. They don't get frustrated if they find out they were on a red herring, and they start looking for the information they missed. I've played with these sorts. You go from worrying whether you can keep the game on track, to wondering if there is any mystery they won't see through in the first hour of play. They become preternatural mind readers, and you have to work hard on your poker skills just to keep from giving things away.
There is generally only one solution to a mystery. The trick as a DM is to make sure that there is more than one way to get there. Although the essay you link to is pretty good, the rule isn't '3 clues' however good advice that may be. The rule is 'clues in all directions'. If you put three clues to pick up the trail, but you put them all in one location along one avenue of investigation, you created another chokepoint. You have to have ways to get the players back on track of the right solution. Each red herring needs to led to its own bit of vital information that might help out. You need to try to figure out what wrong paths the PC's might go down. Chase enough red herrings and a picture should eventually emerge. You also probably also need to plan for the possibility of failure. In other words, what happens if the PC's don't save the day or get the wrong person? In most cases, life goes on and the adventure that they screwed up just lies in wait for another day. You've probably inadvertantly created a reoccuring villain.
If I had to recommend against anything in a mystery its very tight timelines. Most of the games of this sort that I've seen go wrong have rigid timelines where the players have to figure out something by some time (and I've seen many published scenarios with this flaw in spades). That almost always goes wrong unless the DM is experienced enough to see the problem ahead of time and fudge or plan accordingly.
They get frustrated and bored as all their exciting plans turn out to be dead ends. They stop looking for interesting, inventive ways to solve the problems...
What a minute.... "interesting, inventive ways to solve the problems" does not equal "imagining a problem you might be able to solve and then assuming that this problem is that problem". That's the exact opposite of an interesting and an inventive solution. It's rewarding player laziness.
...and end up resorting to rolling dice -- hopefully well enough so that the DM will give them the obscure and specific answer they can't quite figure out on their own.
Whatever. I see where you are going with that, but I'm assuming that we are playing with adults here. Run with the whole 'the players aren't Sherlock Holmes' concept, and pretty soon it turns into, 'the players are stupid' and 'treat your players like children'. While a certain amount of success illusionism is probably inevitable because pretty much every scenario in a long running game is stacked in the players favor, at some point this 'chumming' takes away all possibility of real success and for my part, I tend to figure out that the DM is doing this really fast, and generally, once I do, I start finding excuses not to play. If there is anything worse than being on a railroad, its a DM that won't let you fail.