Some. Some RPGs. Sure. But if it's only some RPGs then that story with all its features isn't central to RPG play generally, but rather an intentional product of certain RPG rule sets.
Yes. I've been saying this a lot - most recently in multiple posts across two threads; but on these boards for 15+ years!
Trying to make sense of the game play that Gygax describes in his rulebooks through the lens of
story is, in my view, somewhere between
misleading and
hopeless.
That doesn't mean there's no
fiction, no
imagination. Of course there is! But it's not about
story. Anymore than the sort of imagining that we might do when we think about how we would prepare for a cross-country hike is storytelling.
For more clarity, I see my view - which isn't original to me! - as having a second implication, that is a type of mirror-image corollary of the implication I've stated in the preceding two paragraphs. Namely that, just as some RPGing is not concerned with
story and some RPG systems are not oriented towards story, so other are. And thus, if you want your RPGing to reliably produce story as an element of the play experience (and not just as a sequence of remembered imaginary events) then it is worth paying attention to those RPG systems.
I think you'd have to do a lot more work to prove that even allocating roles is somehow less efficient than not having them. As far as the goal of freeform play goes I think you need to account for the setting itself in addition to the doings of certain protagonists. Exploring the setting itself (and I don't just mean physical exploration) is very much central to RPG play. The actions of the players are obviously also key, but don't really cover things like "let's find out what's behind that door" or "I wonder what the odd scientist is up to?". This is the bit I always assumed your use of "play to find out" at least in part referred to.
Let me try to explain this in a different way. I am Biff the fighter, and I'm in a dungeon room with my trusty compatriots, and there is a closed door. I declare that Biff will open the door to find out what lies beyond. The GM them narrates the new scene. Do we really think that at any point there that the thing being imagined is Biff physically opening the door, or that the picture being built in our imaginations by the GMs subsequent narration is somehow centered on the (currently inactive) player avatars? I don't think so, or at least it's not obviously the case. The GM describes the room and its contents plus atmosphere and whatever and that is what the players are imagining. This example covers lots of situation in lots of different RPGs.
I'll cheerfully admit that
the doings of certain protagonists is at best a loose description of some RPGing. But I can substitute
the nature of a fantasy world; or some more complex state of affairs with a more elaborate description; and the point about efficiency of means still holds.
This comes through in your example: gating the description of a room behind one person's account of how a particular person opens the door to that room is not the most efficient means of establishing the state of affairs that
a group of people is collectively imagining the fantastic contents of a room. The most efficient means is to just read aloud the room description to everyone.
And another point for the sake of clarity: I'm not being facetious here. Compare a Choose Your Own Adventure or Fighting Fantasy-type book, to a LotR Appendices-style listing of all the events and contents of the book. The latter is a more efficient way to bring about the state of affairs that someone is imagining that stuff. But doing it as a game is less efficient. And the less efficient means are what make it fun - for instance, they create the need for decision (which is fun) and the possibility of a particular type of suspense or uncertainty (which is also fun).