I don't know if any of you are actually working on Literary Theory (professionally or just Goodreads/ TV Tropes). I do both of them (sorry, but it's in Spanish). I'm not trying to sell you an Authority Fallacy, but the fact is that there is enough evidence to say that world construction (and the rules within) are actually a hell lot of important in order to determine the genre and its narrative conventions (check out also Mendlesohn Rethorics of Fantasy). In this way, "In-world rules" are genre conventions too.
Look at fantasy writers: Tolkien, Martin, Jordan, Bodoc, Gorodischer. They actually work a lot to construct their worlds and their verosimiles, which allow their stories to function in their own genres within a coherent mainframe. A laser gun, or even a Fireball, in A Game of Thrones would break the verosimile and genre conventions, as well as it would modify the narrative structure. So I will say too that the above statement (about narrative vs world) is blatantly false, as is the claim of the obstacles vs narrative consequences. Obstacles are actually a way of constructing narrative tension, and to encourage taking decisions too. They are also the chance to shine of several classes outside combat. In fact, thanks to the direst consequences of fighting in 5 ed (the drainage of resources is severer, and there is a good chance of a fight going bad) the choice becomes more legitimate.
In fact, there is where the DM agency comes around. Does the DM want to encourage problem resolution? Or does he want to encourage bravery and bold action? Or to make significant the skill sets and differences between characters (for example, giving world significance to the fact that the Fighter is stronger than anyone else).
Every approach works perfectly with the worldly DC resolution, which absolutely can escalate. And The 20th level wizard can admire how well the Fighter saves the children from drowning boldly swimming against the flow, with a good or not that good chance of success (depending on the table's interest).
In several ways, magic is never enough to solve every problem partly because the spells don't last forever, and partly because they have a limited application. There is where the skill checks become relevant. And the Bounded Accuracy and Proficiency rules are there too to make the stats very important, on pair with the powerful feats, because a miserable +1 actually is a lot here, not that much the level or the skill points (because they are gone). Being trained or not makes the difference here. Also, it is here where the superior ASI of the fighter means a lot (and hence, the RA ability comes around with a magnificent +2 to non trained skills). DM agency, here, means keeping true to the genre conventions and the "world" conventions. When and how or why make a skill check is up to the DM (and hence, the table, the players).
Being trained or not is relevant narratively (the strong sailor is expected to swim better than the squishy bookworm wizard, no matter the level to make a narration diverse and grounded) and table-wise, and if a non trained but higher level character have the same ammount of success (high, low, whatever) than my well trained, stat strong character, I would be extremely angry, and maybe I'll punch you on the face before leaving. Why do I waste a resource if, in the end, it does not matter, only my level? Where is the difference between playing a magician, a rogue or a fighter, or to train an ability? And narratively, it generates different tension if the bookworm, no matter his lack of training, for pure heroism swim against the flow, whereas the sailor don't dare.
It's funny though because I've noticed a lot in 5e due to bounded accuracy the big Fighters failing to smash down doors and the Bookworm Wizard getting lucky and smashing it down. Not everything is a skill check (athletics, etc), many things are ability checks, and then the difference between a level 20 and level 1 is really only +5 at best.
The DMG even talks about this a bit and offers different ways to deal with it, but those ways also offer unsatisfactory results, as you go from a wildly unpredictable system to one with too much predictability.
That's where 5e starts to unravel a bit.