Collective world building through narrative results in a story that, if it goes for a while and is actually mentally examined which it probably won't be, at best results in something like 'Lost' or 'X-Files'. It will be disjointed, rambling, and often incoherent and contradictory. Chekov's Guns will be introduced and rust unfired and forgotten. Plot lines will be introduced with bangs and then never touched again. Things that ought to have huge meaning and implication for the setting and the characters will appear by 'rule of cool', or as deus ex machina, or techno-babble resolution, or as McGuffins - and then disappear, their implications and meaning never explored.
Of course, the same sorts of problems can happen with any sort of bottom up world building and all RPGs are always at least partly bottom up. And any well planned story is still subject to whim and randomness, and ought to be subject to whim and randomness because what's the point if the players are on rails?
The only benefit of leveraging the players as world-building resources is it creates the illusion that you don't have to do the hard work of carrying a story along as the GM. It appears to alleviate the need for all that sweat and blood you have to shed to create a world.
The cost is simple. You go from the experience of being within a fantasy story - maybe a bad fantasy story but hopefully a good one - to the experience of being one of a team of screenwriters hammering out the draft of a screenplay around a table. It's not possible to be in the story you are creating. GM's are never immersed in the story the way a player is or can be. If you make everyone wear that hat, then every one is interacting with the story primarily at the meta level.
Or in short, it's no fun to read a 'choose your own adventure' book when you are not only making the choices, but you are writing out what happens as a result. It's for those as yet unseen pages that you are reading and rereading the book. As soon as you know the book well enough that you know what each choice results in, you put it down. The story teller takes vicarious pleasure in their discovery and invents as needed, but he cannot discover anything for himself. The reader explores the story, but cannot create anything beyond his own unique narrative path through the story. Though that path, the reader has (hopefully) a grand adventure and experiences what would otherwise be impossible - living the life of an adventurer through that adventurer's eyes.
If you try to violate that, no one at the table has that last experience. Everyone ultimately has the experiences of working out what the pages in the story are, which is a very different thing. There was recently a very good episode of Wil Wheaton's tabletop where they played FATE that's definitely worth any GM's time to spend some time analyzing the play.
1) There is a famous trope in D&D (so famous, it merited an page of 'Order of the Stick') where during the fortune step, players begin hunting for fiddly +1 modifiers to their roll, that ultimately end up totally changing the resolution. This is generally considered a fiddly undesirable (if inevitable) gamist step of the game as players understandably struggle to achieve as much narrative force as possible. Compare with the actual use of aspects at the FATE table. Is there really a large contrast, or is the primary excitement of an aspect in play basically the same as the player remembering his +2 flanking bonus or the +1 morale bonus he has from the cleric's prayer spell, and changing his own fortune?
2) For all the cool trope-y goodness that went into naming the aspects, how many times in the whole episode were aspects really invoked for their narrative impact rather than their mechanical impact? How many times where the aspects invoked in such a way that the name really mattered to the story, compared to the times that the aspect needed to be fit to the story. For me, it was absolutely jarring to see these little ideas that wanted to be nourished, and grow, and one day be part of a real story, to be slaughtered like so many lambs for their mechanical crunch no matter how vague and ill-fitting their role was in the story. In the background, I think I heard 3x5 note cards weeping.
3) I often suggest that what makes a game fun is the illusion of success. That what any sort of game offers is the experience of being successful at something without nearly as much risk and hard work as real success has. What these collaborative techniques seem to offer is the illusion of success at story building. Nowhere did this feel more true for me than the moment the GM invokes the trope 'Better Living through Chemistry' to send a protagonist literally to Hell... for just one 'round', in a way that was so meaningless, that even the player understands that despite having disappeared literally into Hell, this literal arrival in Hell has no real impact on the story and he'll arrive again back in the 'real world' largely unscathed (and barely changed) as soon as it is his turn. While there is profound ego stroking going on there, there really isn't anything else going on related to story. True 'Shining Moments of Awesome' require more investment than that, so that the moment is a true payoff of something that has mattered to the story for a very long time. They require resolution of a conflict. But no conflict was invoked, just something called 'Better Living through Chemistry' and literally going to Hell was what... better living through chemistry? Only an RPG could get away with that sort of thing. If it happened in a novel, you'd be going, "Wait a minute... this seems like it ought to be an important plot point..."