But I absolutely would not want the game to revolve around such approach. At that point it becomes more like collective storytelling around some rules like Once Upon a Time (card game) and less like a tabletop RPG.
Burning Wheel is a tabletop RPG. It's no more "collective storytelling" than is D&D combat. It's just that it extends the principle of "finality" that applies in D&D combat to other areas of character activity.
To me the whole point of having the GM there is for them to use their judgement. I want them to come up with interesting things I want them to come up with surprising things and I trust them to do it better than a codified rule system could.
This is why Burning Wheel has a GM. The GM uses his/her judgement (see eg the GM deciding what happens when Thurgon and Aramina fail to command Rufus). The GM comes up with interesting things (eg deciding that Rusus is on his way to pick up wine for "the master"). The GM comes up with surprising things (eg that Thurgon's younger brother has gone south in search of glory).
But Burning Wheel also has players who are able to exercise agency: they can declare actions for their PCs, and if those actions succeed then the GM is bound.
And when I play a character, I don't want to be deciding setting details because that forces me constantly from in-character perspective to the narrator-perspective.
Notice how in the example of play I posted there is not point at which I (as the player of Thurgon and Aramina) ever had to switch from an "in-character" to a "narrator" perspective. All I did was say what Thurgon and Aramina were doing.
This is a recurring feature of discussion on these boards: one poster sets out an example of, or an account of, RPGing that involves player agency; and another poster responds by expressing his/her dislike of
quite a different thing (ie shared storytelling and narrator perspective). I don't quite get why.
The rest of the world reacting to the PCs' success doesn't (or really shouldn't) change or negate the success. If they defeat a baddie in a permanent-seeming way, that baddie should stay defeated. If they (to use your example below) convince someone to their side, they should stay convinced.
And if the PCs convince Pup to do something that weakens his followers' allegiance, I think the GM is behaving reasonably to have the followers become less loyal or shift their allegiance. The PCs have changed the situation, and the shared fiction; it's just changed (again) afterward--as situations tend to do.
Suppose, in resolving a D&D combat, the player declares "I attack the Orc with my sword", and rolls to hit. The GM is not at liberty to just decide that the Orc blocks the sword-blow with its shield. The GM can only narrate such a thing
if the roll to hit fails.
In Classic Traveller, if a player has his/her PC attempt a tricky manoeuvre while wearing a vacc suit, the GM is not at liberty just to narrate that the PC gets stuck or catches an air pipe or similar. There is an action resolution subsystem for this, and only if the player fails the check is the GM at liberty to narrate the dangerous situation coming to pass. (The resolution system then goes on to specify the check required to get out of the dangerous situation without damage to vacc suit ingegrity.)
What might weaken Pup's followers' allegiance? Who knows! If the GM has declared that
Pup is in control here, and if the players have then successfully brought Pup to heel,
they have taken control of the controller. The GM is not just at liberty to decide Pup is no longer the controller. That would have to be the outcome of something else going wrong for the PCs - at which point the GM is free to indulge his/her conception of what sorts of things might weaken the followers' allegiance.
The idea that
the GM is free to make up whatever fiction s/he wants regardless of the outcomes of action resolution is anathema to player agency. Because it makes action declarations pointless: whatever they are, and whatever follows from them, the GM can do what s/he likes!
And to head off the recurrent question,
so what is the GM for then? Not all action declarations succeed. When they fail, the players have forfeited their agency to the GM. That's (roughly) how winning and losing rolls goes in a dice-based game!
And sometimes it's not clear what happens next. In a RPG with a GM, that's where the GM has a special role to set the scene ("framing"). But framing need not negate or disregard player agency. It can easily honour it.
To follow on from what
@Ovinomancer said not far upthread, if the players look to the GM to see what happens next, and it's clear that the PCs have been pushing Pup around, the GM can tell them that
Pup's followers are starting to mutter among themselves and give you surly glances when they think you're nor looking at them. Now the status of Pup's followers has clearly been put at stake, and the players can decide what (if anything) their PCs do about it.