Why has the GM introduced this obstacle? What trajectory of play has brought it about that the PCs
must overcome this obstacle to achieve the goal of arriving at such-and-such a place?
Until we understand the logic that underpins the framing you have described, how can we even talk about its resolution in (say) 4e D&D, in Dungeon World or in Burning Wheel?
Here is Manbearcat making the same point:
Here's a different illustration, from Burning Wheel. I'm quoting from p 269 of Revised, but the text is the same in Gold and Gold Revised:
Finally, there is the sacred and most holy role of the players. In Burning Wheel games, players have a number of duties:
*Prime among them is the responsibility to offer hooks to their GM and the other players in the form of Beliefs, Instincts and traits . . ..
*Players in Burning Wheel must use their characters to drive the story forward . . .
* 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 with a Dark Elf assassin. 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.
Here are some concrete examples from actual play:
*My GM has a thing for Elves. Some Elven NPCs turned up and helped my PC and his sidekick with some Orcs. The Elves wanted us to join them pursuing more Orcs. I wanted the Elves to join me in liberating Auxol, my ancestral estate. So I called for a Duel of Wits to persuade the Elf. I failed miserably (poor stats, and probably poor scripting too) but I achieved my goal - that play was not about the Elves issue with the Orcs, it was about my issues with my family and our estate.
My sidekick had as one Belief that "I won't *end my career with no coin and no spellbooks" (or very much along those lines). So I decided that she recalled that Evard's tower was nearby. And I invoked the mechanics - in this case, Wises checks - and the GM worked out the obstacle to recall the location of Evard's tower using Great Masters-wise and I rolled the dice and succeeded; and after some debate between my main character and my sidekick (played by the GM in the Duel of Wits) we travelled to Evard's tower.
*I decided the time had come to return to Auxol. I said to the GM, "Now that we're on the borders of Auxol I wonder if we'll meet any of my family members?" And we worked out the obstacle, and I rolled the dice (Circles plus relevant Affiliations) and succeeded, and we met my brother. That encounter, and the way it played out, was perhaps the most intense roleplaying I've experienced in 40 years in the hobby.
This is a framework for play that is completely different from 5e D&D. The role of the players, and the role of the GM, are completely different. The rules for calling for a check, and who can call for one, are completely different. The principles that govern the framing of scenes and the narration of consequences are completely different.
Could someone try and emulate BW using 5e D&D? Maybe - use Bonds, Ideals and Flaws in place of Beliefs, Instincts and traits; use INT instead of Wises, and CHA instead of Circles; use "say 'yes' or roll the dice" as the core principle for calling for checks. I've never heard of anyone doing this, but maybe it's going on out there. There will be obvious problems that crop up, beginning with the fact that by default, in D&D, casting spells doesn't require a check at all. Perhaps those tables who are doing this have come up with workarounds - I don't know, because if they exist they're utterly invisible to me here on ENworld.
Could someone try and emulate 5e D&D using Burning Wheel? I think so, but you'd have to drop "say 'yes' or roll the dice" as the core principle for calling for checks, and you'd have to completely change the way Wises and Circles work: the former would become 5e-like knowledge checks, and the latter a type of Streetwise skill.
Personally, I think the "hacks" to BW would be easier than the hacks to 5e D&D. But in any event, I don't think these possibilities of drifting change the fact that the RPGs, as presented to their readers and players, are radically different in the ways I've described.