Often, there is mystery in an adventure. The mystery, whatever it is, is learned at the climax of the scenario. It will be something perplexing the players. And, that's good. A GM wants players to be involved and perplexed.
But, if the players can just spend a point and learn the mystery, or get enough clues and context so that they figure it out early, then poof goes one of the main pushes for the adventure.
In addition, it's very meta-game, too. Why would the characters suddenly know this information when they didn't know it before--especially if no character has a skill (or high enough skill) to know the mystery.
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That sounds like a player will spend a point--a precious resource--and get nothing for it, because the GM is so cryptic,what he says doesn't help and keeps the GM's mystery hidden.
Again, I don't think this is a good mechanic to have in a game. Not unless the GM is ready for it, as with a fortune teller, soothsayer, or oracle.
Wow... you've really misconstrued what this is for. I'd also hate to take part in any mystery-focussed game you're GMing, if you're only willing to parcel out information on your schedule. The mystery shouldn't just be revealed at the end; the players should be the ones to figure it out, from the clues they glean and the information they obtain. Otherwise they're just mute observers to the GM's story, rather than active participants.
How is it metagame? Sure, taken without the context of the surrounding environment (the situation a skill test was taken in, for example), it could look metagame, but otherwise you seem to be bandying that term around as a generic "bad thing" without any particular justification. Of course characters will gain information that they didn't have before - that's called being observant, making insights, and learning. As situations and circumstances change, new things presented to player characters will add to the information they already have; consequently, a player character will have more information, and more opportunities for information, as the adventure progresses.
Determining if the players have sufficient skill to know the mystery... that's what the skill test, and the Momentum spend are for - it places a cost on knowledge. It is a mechanism by which players can be rewarded for successful tests with knowledge about related things, the way both real people and fictional characters alike come to realisations, uncover previously unknown information, or make deductions. I'm actually shocked that I have to explain this to anybody, given how fundamental it should be to the very process of playing an RPG - the players talk to the GM, who acts as the player characters' senses in the world and describes what they see, hear, and otherwise sense. Have you never honestly seen a player in an RPG attempt a skill test to gain information, because I find that inconceivable.
Will it require effort on the part of the GM? Yes, but no more than is involved in the preparation of any other adventure. Will it require extraordinary preparations, such as ensuring that there's an oracle or fortune teller present? No, and I can't honestly believe that anyone would come to that sort of conclusion unless they were deliberately looking for opportunities to complain. It's a mechanic that formalises something that I had regarded as commonplace in RPGs, for when players take skill tests intended to obtain knowledge - through research ("a few hours studying ancient scrolls tells you that..."), through their character talking to NPCs ("after an evening plying locals with ale and questions, you discover that..."), and through simple observation of their surroundings ("you spot a familiar symbol on the clothes of your assailant...")