What conflict resolution (especially the more moment to moment sort seen in Apocalypse World) does is it continually volleys the ball back to the GM to frame situations/scenes that speak to the premise of the game or the characters. Task resolution inherently results in focusing on things outside the core premise of the characters and/or game. When I run Masks I'm always making GM Moves that speak to what's come before, but also bringing in new elements that are relevant to the characters (address their personal situations, reputations, come between player characters, etc).
This isn't, in my understanding, a function of the GM. It actually can't be, unless you conflate several different GM roles that I would view as being professionally firewalled. Setting up all of the pieces and then moving the ones you're supposed to control are separate jobs that simply reside in the same person. Situation is the result of chains of actions from the PCs and those NPCs. Setting up an interesting board for all of those actions to happen on is fairly difficult, and the sort of thing GMing advice is theoretically supposed to teach you how to do, plus ideally you want a series of tools to let you try and evaluate likely outcomes (things like CR in a combat focused game, or even things like a faction-specific list of goals). The actual progress of what does happen is down to system though, it's a result of player choices being fed through mechanics to see the results, which, assuming sufficient GM honesty, sufficiently detailed rules and sufficiently engaged players, should allow players to push an agenda into the situation.
Pedantic, your post doesn't make sense to me. I mean, what
@Campbell describes is, literally, the job of the GM in Apocalypse World. And I assume Masks, Monsterhearts and similar games state the job of the GM very similarly to AW.
What Campbell says is also a pretty good description of the job of the GM in Burning Wheel, even though BW uses a different set of framing and resolution techniques from PbtA games. I mean, here is some of the relevant text from the BW rulebook (Gold Revised, pp 9-11):
In the game, players take on the roles of characters inspired by history and works of fantasy fiction. These characters are a list of abilities rated with numbers and a list of player-determined priorities. . . . Expressing these numbers and priorities within situations presented by the game master (GM) is what the game is all about. . . .
There are consequences to your choices in this game. They range from the very black and white, "If I engage in this duel, my character might die," to the more complex, "If my character undertakes this task, he'll be changed, and I don't know exactly how." Recognizing that the system enforces these choices will help you navigate play. I always encourage players to think before they test their characters. Are you prepared to accept the consequences of your actions?
The in-game consequences of the players' decisions are described in this rulebook. The moral ramifications are left to you. . .
Burning Wheel . . . is inherently a social game. The players interact with one another to come to decisions and have the characters undertake actions.
One of you takes on the role of the game master. The GM is responsible for challenging the players. . . . Everyone else plays a protagonist in the story. . . . The GM present the players with problems based on the players' priorities. The players use their characters' abilities to overcome these obstacles. To do this, dice are rolled and the results are interpreted using the rules presented in this book.
The GM's job, in BW is emphatically
not to "set up an interesting board" and then "move pieces". This may not be to your taste, but that doesn't mean that Vincent Baker, Luke Crane etc are confused in their game designs, or in the instructions they give to the GMs of those games.
Conflict resolution is disempowering to the player; they can't influence what is "framed," and they get so little say in the resolution, because it's always down to one test. You don't have a lot of agency to affect the outcome, and the situation is so transient before the next concern occurs. My sense in those games is that the player isn't supposed to care; you aren't supposed to want any given outcome or drive to any result, the "drive like a stolen car" concept. Instead, you're there to engage with the premise, the real act of agency was agreeing to play a game about X in the first place.
This doesn't make any sense to me either.
First, as
@soviet pointed out, your "down to one test" claim is just false. Burning Wheel has linked tests, and also complex resolution via Fight!, Range and Cover, Duel of Wits, and the rules for pursuit. In AW, as the example of play in the "Moves Snowball" chapter illustrates, the resolution of one player-side move can easily feed into another.
That AW example also shows how it is not true that the player can't influence what is framed: in "Moves Snowball" Marie's player first Reads a Sitch, which does influence what is framed - by obliging the GM to tell her who is the real threat here - and then declares further actions in the context of that scene.
In Burning Wheel, when I play, I influence how scenes are framed all the time. First, I sometimes tell my GM what would be interesting! And as per the instructions to players, I also declare appropriate actions. This is from the Revised rulebook, p 269; the same text is also in the Gold rulebooks:
Use the mechanics! Players are expected to call for a Duel of Wits or a Circles test or to demand the Range and Cover rules in a shooting match . . . Don't wait for the GM to invoke a rule - invoke the damn thing yourself and get the story moving! . . . If the story doesn't interest you, it's your job to create interesting situations and involve yourself.
For instance, I declare Circles checks, or Wises checks, or try to persuade NPCs via Duels of Wits, or whatever.
So far from not caring, I am always trying to drive to a given result: this is part of inhabiting my character, and declaring actions that are the things that character would do.