Because, functionally, you'd have to rely on the GM or table consensus to create the resolution mechanics to give this teeth. 5e, and I'd argue AD&D, lack any way to resolve conflicts that have teeth. There just don't exist the kind of mechanics to do this. Instead, you have resolution mechanics that are divorced from intent and focus on the atomic nature of task resolution, and I find this fights against playing the game in this way unless the table just decided to implement some kind of additional rule structure for how to pass the conch or resolve conflicts of intent.
I think there are two ways of looking at this.
If I'm comparing AD&D, or Rolemaster, to Burning Wheel, than the contrast you describe is evident. All give you characters; those characters have various numbers on sheets associated with them (for fighting, for talking - that's CHA in AD&D, etc). But the first two are pretty rickety in their action resolution structure.
But not hopeless. For social interaction, as an example, AD&D has a reaction table, modified by CHA, and that can be used to resolve approaches by PCs to NPCs. (I do just this in Classic Traveller.) Rolemaster has the Influence/Interaction table (this is from RM2/RMC Character Law):
-26 down: Your blatant attempt at coercion alienates your audience. They are infuenced to do the opposite of what you were attempting to get them to do. Until a change in circumstances occurs, any attempts by to to infuence them will fail.
-25 to 04: You audience rejects you, causing you to lose confidence and your air of authority. Any influence attempts during the next hour will result in failures (see 05-75 below).
05 to 75: You have failed. Your audience will not be receptive to any of your attempts at infuence for at least 1 day.
76 to 90: Your audeience is still listening. You can continue to try to influence them.
91 to 110: Keep talking, your audeince is becoming more friendly. Modify your next roll by +20.
111-175: You have influenced your audience.
176 up: Not only did you influence your audience, but you receive a +50 bonus on influencing them until you do something to cause them to lose confidence in you.
Modifications: Difficulty [from +30 Routine to -70 Absurd]
+50 - Audience is personally loyal or devoted to the character
+20 - Audience is under hire to the character
+ Skill bonus for Influence and Interaction.
Note: Difficulty and other modifications are based upon the basic attitude of the audience towards the character and upon what the character is trying to get them to do.
Ultimately, what gives teeth to resolution in BW is
intent and task together with
let it ride. AD&D is not inherently unable to incorporate these.
Oddly enough, 5e might be less amenable to "vanilla narrativism" than AD&D: it doesn't have a set reaction table like AD&D (or Traveller) and so needs the GM to set a DC for interactions, which is perhaps less certain/stable and doesn't produce the "intermediate" results that a typical reaction table does. But couldn't that be worked around?
Another issue with 5e is the one I mentioned upthread to
@hawkeyefan: there are abilities like the Folk Hero one, or Rangers' favoured terrain, which are (in my view) a bit unclear as to what their actual function is and hence put a lot of decision-making pressure on the GM; AD&D and RM don't have this sort of thing.
There are knowledge and perception-type skills in all these systems. But that's not fatal. Prince Valiant does too, and yet can work with pretty light-touch prep. And in the context of D&D, there is so much published material available it's often not going to be that hard to pull out a map or room or similar, with perception used to spot hidden things and/or people. Investigation probably becomes a pretty unhelpful skill in low-prep 5e D&D, but that's a modest casualty.