I would put it a bit differently.
There is a type of human creative endeavour called storytelling. It includes certain elements which can be understood at least semi-technically: characters who have dramatic needs; rising action; perhaps most importantly crisis or climax in which the question of whether the character will fulfil their dramatic need is posed and answered; and, as a result, resolution one way or another.
The appeal of RPGing, for me at least, is that it enables the creation of stories with (i) no one having to be the storyteller, and (ii) the possibility of having the experience of "being" the character. This is a distinctive type of aesthetic experience.
Key to achieving (ii) is to have PC build establish dramatic needs for those PCs. These are the player priorities that I have talked about in this thread. And I've said a bit about how various RPG systems permit players to express them (eg player-authored quests in 4e D&D).
Key to achieving (i) is to have a system for framing, and for resolution, that will make dramatic need salient without anyone have to choose, in advance, what the resolution of those needs will look like. I've given examples, and explanation, that show how certain GMing principles can achieve this. (There are other RPGs with principles that are a bit different from what I've discussed that can also do this, most prominent Apocalypse World and some of its offshoots.)
The alternative approach being set out in this thread, in which players play characters who are to a significant extent self-inserted lenses whereby they learn what the GM has in mind for the fiction, and prompt the GM to present and develop those ideas, is to me a quite different experience. It involves comparatively less creative engagement from the players. Their role is to provide characterisation for their PCs, and to unravel the "mystery" of the GM's world - to work out how it operates, what its various components are and how they related, etc. Players, in this approach, perform a role that is more cognitive than creative.
Nicely articulated. I've been attempting to advance some related theory and this is roughly where I am at present.
1. At least two human creative drives find expression in TTRPG -
storytelling and
exploration.
2. Players engage with these drives in a ludic-duality - at once
audience and
author. This ludic-duality makes experiencing content in the form of game distinct from experiencing similar content in other mediums.
3. Norms of play have formed around
weightings of the duality - either more toward audience, or more toward author. This is only weight, neither is absent.
So to consider some pairings
i)
Storytelling=audience. This mode maps to forms of trad play that prioritise a satisfying story. Players are pre-destined protagonists in a story told by game designers and/or GM. Perhaps it is the most naturally obvious mode (to engage with games in ways familiar from other media.)
Ii)
Storytelling=author. This mode maps to what you have described. Participants collaborate to create their story through play; it emerges in a dramatic situation presented by game designers and/or GM.
iii)
Exploration=audience. This mode maps to forms of trad play in which players explore content prepared by game designers and/or GM.
iv)
Exploration=author. This mode maps to forms of sim play that leverage the collective genius of participants and irrealities of subject. Participants collaborate to investigate subject through play, typically one nominated by and with tools provided by game designers and/or GM.
I'm reminded of the lean-back / lean-forward dichotomy of video / games. One is receptive - let me experience something - the other is active - let me make something happen. These preferences can move around the table and change over time. In a similar vein, no one is assumed to do pure storytelling or pure exploring: the two are mixed in varying degrees.
Finally, there are techniques connected with the specific properties of TTRPG that can serve any pairing. Such as
a)
Fiction-first. TTRPG is distinct from other games in heavily committting to a fiction state (along with a system state.) Fiction-first most importantly observes the continuous flow of momentum back and forth between them.
b)
Internal-cause. In fictional realities, extrapolating from world laws strengthens immersion (and avoids jarring disjunctions.)
There are others, but I felt those two worth listing provocatively in just this way. Related to the thread topic, I think what counts as ideal player agency shifts according to the preferences outlined above as pairings (actually a continuum).