Hey! Your sig here almost sounds like the preference for a player-driven game over a DM-driven one!
Ay, marry, there's the rub! The unknown task is in fact known by the DM ahead of time - it's part of The Grand Plot - and the hope* is that the PCs will either a) somehow stumble onto it, realize its relevance, and do it; or b) do it without ever knowing what they've done until later when the relevance becomes more clear.
* - and if they miss it completely, no problem; it'll reappear somewhere else later.
I still don't get why you feel this way. Using an example from my own Dark Sun game scenario, two of the PCs have goals at the beginning of play as follows: The Fighter, a former arena slave, desperately seeks her combat partner, who disappeared during the insurrection and slave uprising that immediately precedes play. The Druid mechanically has a theme called "Ghost of the Past," through which we flavor the theme power as a mystic connection to Athas's past--glimmers of the distant past when the world was green, before the scorching sun turned (nearly) all to desert. Her goal is to somehow use these intuitions of the past to discover a way to bring some kind of healing to the planet.
Perhaps you might frame the Fighter's "drives" as "emo," in the sense that they are rather personal (though outwardly directed). But the Druid? How is that anything less than the grandest of scales? And note that neither of these "narratives" are DM-written. They are PC goals and the scenes that I, as DM, will frame will be interesting obstacles, etc. along the way as the PCs take actions to meet these goals.
The Druid's goal is great - that's the sort of thing one can build a good long multi-faceted campaign around! Excellent stuff!
The Fighter's goal doesn't give much to work with - it can easily be solved in one adventure, if that. Then what do you do?
You know, as I type this I'm having a thought or two (alert the media, it's a rare occurrence!). Would it be the end of the world for the player to not only come up with a goal but to give a high-level storyboard at least ten adventures long* on how that goal might be achieved in the game? That's the player-drive side and with luck it'll force goals more like your Druid's and less like your Fighter's. Then, once the DM gets all these storyboards she takes them and merges them together (without telling the players exactly how she's doing so) into something of a master storyboard for the campaign, while perhaps throwing in a few ideas of her own. That's the DM-drive side. Then she runs the game in whatever manner she likes on the day-to-day scale, and it's up to her whether she informs players which adventures tie to whose goals or whatever.
* - an example of what I mean for the Druid in your game: (I suppose you could call these chapters instead of adventures, but whatever)
GOAL: Encounter Ghost of the Past intuitions and then to somehow use these intuitions to discover a way to bring some kind of healing to the planet.
STORYBOARD:
Adventure 1 - introductory, learn about the other party members, the setting, etc., including history that says the world was once a green place. Dungeon crawl with extras?
Adventure 2 - encounter GotP intuitions at some point, maybe learn what they are (this can be mostly someone else's adventure, my bits can be a sidebar)
Adventure 3 - learn of an item that relates to these intuitions, also start discovery process as to what they mean (another dungeon crawl followed by research)
Adventure 4 - find the Green Crystal: this clarifies the GotP intuitions, tells me I still need more (the intuitions by themselves aren't enough instruction) - typical item-recovery mission
Adventure 5 - locate then recover (then decipher) the Prophecies of Athasia, in effect the rather cryptic divinely-placed instructions on what to do and what is needed - and it's not in a safe place!
Adventure 6 - the Grand Oasis - nobody knows why it's where it is or why it's always green; in fact it's all that remains of what was once a divinely-blessed forest, a piece of which is needed. The adventure is the journey there and back and encounters in the settlements surrounding it, very dangerous.
Adventure 7 - plants need water - maritime adventure where we sail to find the fountain of youth (base the events on Pirates of Caribbean 4?) and recover some of its waters
Adventure 8 - to find the last surviving Ent on the planet, a small part of whom is necessary both to green the planet and contunie his race (dangerous forest adventure)
Adventure 9 - off-plane travel to gain direct divine blessing on parts gathered; danger is the astral journey there and back
Adventure 10 - grand finale - heal the planet and make it green once more. Many people oppose this, so a big sprawling adventure maybe in several parts? Civil war? Battlesystem-type stuff?
You see what I'm after here. Each player gives in something like this for their character, and the DM then synthesizes them into something vaguely resembling a campaign combining adventure ideas where she can. For example, if someone else also needs a written work maybe the adventure to find that can be combined with the Prophecies of Athasia adventure (or maybe the Prophecies can do for both?).
And the "final" storyboard built by the DM will never be final at all - characters come and go, goals and ideals change, and of course nothing ever survives contact with the dice.
Thoughts?
Lanefan