How about if a player contributes to the shared fiction in another way? Let’s say they have an idea for a goal for their PC and maybe it involves a church of some obscure god and an artifact stolen from the PC’s family.
So the player has added an organization to the fiction and possibly a deity and an artifact and some conflict between that organization and the PC’s family. This is also material that can be explored through play; the GM can pick up these threads and weave them into the unfolding fiction.
Now I know you might start twitching at the mere thought of this, but rest assured plenty of games allow this.
Sure, I get that; and it's cool to have a player thinking this far ahead. In a solo game this would flat-out rock.
In a group game, however, if each player independently comes up with a similarly elaborate series of ideas that don't inter-relate with anyone else's ideas* then everyone has more or less stated they want to do their own thing and the GM is left trying to herd cats; even more so if the things a given player wants to do are of limited or no interest to anyone else.
Taken a step further, in a group game where the general expectations are a) more than one PC per player (such that they can be cycled in and out at the player's choice) and-or b) at least a moderate degree of PC lethality the GM is further left not knowing which cats she'll have to herd at any given time.
On top of this, the GM is trying to fit in any ideas she might have (she gets to have ideas too, right?).
This sounds like a powderkeg of a party, ready to split apart at a moment's notice.
That said, if only one or two players have such ideas and the others are willing to simply go with the flow the obvious risk becomes that those one or two players will end up dominating the game, getting all the spotlight time, etc.
Recipe for at-the-table disaster, I'd say.
* - and if they do inter-relate with other players'/PCs' ideas, chances are very high it's going to appear contrived.
So, knowing that such a game would also allow a PC to open its mouth and speak and for the player to describe the PC and give them personality....knowing that it also allows this most basic form of contribution that you choose to celebrate....would you say that this game allows more contribution to the fiction from the player?
If not, why not?
It allows more contribution to the fiction from the player. My position is that at some point this becomes more of a bug than a feature.