This is true of Apocalypse World too: what move is made on the player-side doesn't change the span of results (6-, 7-9, 10+). Or Marvel Heroic RP: what move is made on the player-side doesn't change the fact that a dice pool is rolled and its result compared to a similar opposed dice pool. Or Burning Wheel (outside of Fight! and maybe Range and Cover) or Prince Valiant or Agon or Cthulhu Dark or In A Wicked Age.
Skill challenges aren't a wargame resolution system. Nor a boardgame resolution system. They're a RPG resolution system. The fiction is central, as the OP states. What drives them is not clever wargaming play but caring about the fiction, engaging with it, and changing it. Just as in the other RPGs I've mentioned.
I also find it slightly ironic, or at least amusing, that the traditional criticism of 4e, that it's too boardgame-y, has now morphed to be that it's not boardgame-y enough!
I mean, I'm not a big fan of any of those games. Detailed lists of specific skill actions is very much my preferred approach, but we're really into an ideological discussion of what TTRPGs are for.
Fundamentally, I think RPGs differ from board games primarily in that your objectives are unbounded, and player determined. You get to decide what you want, and then roll back to the mechanics to best achieve those outcomes. Trying to optimize for those outcomes is a fun and engaging part of the game, and the same part of the brain I'd use to say, play a game of Barrage and navigate difficult worker placement through limited choices. TTRPGs offer a unique ability to do that, while engaging in a narrative, and while controlling the victory conditions that result from my choices.
There's no reason a skill system couldn't be built with high-agency decision making. You could absolutely present a situation wherein a player has a difficult choice to make between diplomacy and stealth, because both will spiral out into different failure points and tax different abilities (and/or cost different resources) that they have to decide the best trade-offs between.
Combat is mechanically significantly more complex than skill challenges.
Skill challenges are more complex than a skill check.
Skill checks have more mechanics than DM ad hoc adjudication.
These are a continuum with each having advantages and disadvantages for different situations, not a scale of good to bad. DM ad hoc adjudication can be a great part of the game.
Skill challenges are generally for when you want some rolls for an adjudication, but more than just a single decision point and roll.
Complexity is related, but not directly comparable to the kind of decision making agency I'm talking about. "More mechanics" does not lead to more agency necessarily. A 3e Fighter built for tripping, for example, will be playing a mechanically heavy combat game, but will actually have a really straightforward set of decisions to make. The optimization/decision making case will usually be "trip something, then attack it," because that's really all that build could do, and having to do anything else is a failure state.
On the other hand, getting over a wall might involve only a single skill check, but could be a higher agency situation. You might have a viable case for trying to jump it (unlikely but puts you in a better position) climbing it (slower, but pretty easy) or smashing through it (loud, but hey, if you're made of adamantine, it will definitely work and quickly). A player might reasonable choose any of those options to optimize for a specific state they want to be in, because the next skill check they have to make will be advantaged in some other way they believe they can predict.
My preferred resolution system would allow me to adjudicate any of those three choices based on the known state of the fictional world, and then evaluate the game state after they've happened to try and come up with the next best course of action. A skill challenge system would weight them equally, leave the same amount of distance between my character and their goal after the check. The only thing I can manipulate as a player there is the combination of Hard/Medium/Easy DC I'm rolling against vs. the highest modifier I can leverage. It's a trivial problem to solve.
The levers I want to be able to play with are trying to get closer to my goal by trying one action over another, and ideally I'd like to be able to influence what kinds of actions are possible at all with my declared actions. Skill challenges smooth all of that out to a flat plane.
It's easy to resolve, and easier to make declarations about the fictional state around, but it's less engaging as a game*.
*I realize I'm using "game" idiosyncratically here, I'm not trying to suggest anything absolute about what makes an experience gameplay, but I'm striving for language to differentiate the loop of making optimization decisions that is engagement with most games, vs. the narrative/improv/storytelling aspect that is also part of the RPG experience.