Let's take the example, P1 wants to say
But P2 has a different idea, they want to say that nothing can revise the cousin except for a sacrifice on their part of whatever they hold dearest. Is it down to who spoke first? GM helps players navigate such conflicts, applying the rules judiciously.
Well... first of all, what is the underlying motivation of P2's character? I mean, what is more likely IME is that P2 has asserted some kind of character traits/motives/backstory which the GM can put pressure on by asserting that the cousin can only be saved by a sacrifice on their part, or that the need for this sacrifice is a consequence of some resolution process putting forward an adverse result opposing the PC's achievement of their goals.
This is not to say that PC's cannot have these diverse and mutually exclusive goals. In our BitD game last year Takeo was opposed (both as an expression of his backstory/vice and refined during play) to 'demonic forces', but one of the other characters, Tal Rajan, was aligned with such forces! We were all part of the same crew, and there was a score where things got to, basically a head. Takeo had to decide if he would save some orphaned children by accepting She Who Slays in Darkness as a patron, OR basically take on Tal Rajan/split the crew. Now, if it was JUST the integrity of the crew, Takeo might have gone against Tal, but in this case things 'worked out', Takeo discovered which of his priorities were more important (though this choice never sat easy with him) and as a side-effect the crew became more united. I won't say the GM or anyone else planned this, or even leveraged events to make it happen though. It was sheer "play in-character" stuff, obviously with the dice inserting another level of uncertainty.
And lets imagine Takeo had taken up his swords and, say, dispelled SWSID's manifestation? Now maybe Tal would have yielded and taken a different course, or maybe the group would have split, or even annihilated each other right then and there (Beaker would blow us all up, haha). That would have been cool, a bit unexpected and abrupt, but interesting.
What you have to understand with this sort of play is that there's no 'right path'. There's no specific way through to enjoying a certain experience. Anything can happen, and that is meant in a bit different way from what usually comes up in trad play where you could certainly TPK, perhaps, but you won't generally evolve your entire group structure and rationale completely, or even dissolve into factions (I mean, I'm sure someone is going to immediately leap in and give that one in a billion games counterexample, but I don't think it invalidates the general truth of the assertion).
Harmonize may not be the best word, but I mean this. Each player decided who their character was, what motivates them, etc. GM helps them create characters that belong in the same space, and that - in their interactions - enhance rather than disrupt each other's purposes.
I mean, yes, that's true to a degree, the players PCs obviously start out with whatever the game's premise is in terms of their relation to each other and what their goals etc. might be. I'd point out however that many narrativist games use radically different premises than anything you will likely find in trad, certainly of a D&D ilk. Still, the players won't be trying to disrupt the other players, at least not at what you call 'lusory goals' level.
I took clearing in advance to mean something like this. Suppose we're playing RuneQuest: astronaut characters are unlikely to fit well, and it's more likely rune or spirit magic that has the cousin in the magical sleep. The herbs should be considered in terms of their connection with those things, and... the player has told the GM where they want to go and what they want to achieve. Practically begging them to add a twist... "and what problems await you in Townshire? Why did you leave?" Part of the GM's job is to help the player say things they otherwise wouldn't want to say, or say those things for them. They can't protagonise without antagony. Or in sim mode to encourage curiousity "Why would the tyrant need to do that to your cousin? Who is your cousin? How do they figure? What threat did your cousin pose to the warlock?"
It's quite insufficient just to have warlocks doping cousins. Tyrants need motives. Cousins need to be their subject, or have interfered somehow. It's GM's job to make sure those are known. The analogy of conductor is replete with resources for grasping this.
Honestly, it depends. Often we can simply lean on genre tropes and our mutual understanding of what will facilitate play here. Bad guys do bad things, definitionally, etc. Now, that might lead to shallow play, or require some downstream elucidation during play, but as a general point, low myth games at least don't generally hang themselves up much on elaborate plot elements to start with. The cousin needs help, this puts pressure on the PCs in various ways, which the GM will probably double down on over time, etc. Not to get down on the 'GM as Conductor' metaphor, it seems reasonably apt for the most part, but GM is also partly author as well and can use that in a pretty much purely creative way too, just not as unconstrainedly as in, say, trad 5e play.
I very much think they do. They don't just let Jo Harmonica rock up to their classical piece. Not without considering the effect to the whole.
I think this is where the conductor analogy gets off track. The power dynamics are too different.
It holds nicely. That it doesn't seem that way might be down to taking some unsatisfactory version of trad GMing that one has experienced, and reading it into every description of trad GMing. One might as well say that players make proposals to the dice, which do all the actual initiating!
This is silly.
Another version of trad GMing is, as Eero put it "GM story hour"
A group may be blessed to have access to a narrator whose stories they love to immerse in. Who will serve as their lusory-means through which they satisfy their pre-lusory goals. Or, in trad forms of sim, they may be blessed to have a GM working to expand their ludic-agency in the directions they show interest in, just as bedrockgames explained multiple times in another thread. And this really matters, because at any given moment, regardless of whatever set of ludic-agency I might think a player has, they can only avail of a few elements. (This is one reason why playbooks turn out to afford good ludic-agency: not because they are expansive (they are not) but because they contain the ludic-agency the player will want to employ in each moment of play, oriented to the situation and premises of the specific game.)
Having had the experience of being a player in a game run by a GM with huge creative energy and a propensity for completely dominating the subject matter of play, I can tell you it is quite a lot less 'game' than you might think... Yes, he was a 'fan of the characters' in many ways, but his game would have produced much greater potency, IMHO, if he had also followed the OTHER principles of Dungeon World (at least some of them, it was 1e AD&D after all) as well. Overall he was a great GM, but I've also played under 100's of other GMs and not a single one of them was ever even in the same league. I mean that, he was, and is, an extraordinary individual in all ways, not ever to be encountered twice in one lifetime, so its hard to say anyone else should try to borrow his techniques. I never did, and I consider myself pretty good as a trad GM too. I am even better now that I've left that mostly behind.