I've read your discussion with @Ovinomancer about Inspiration and on that I agree with Ovinomancer. The most I can see in that subsystem is that players have a modest incentive, mediated via the GM, to flavour their action declarations by reference to their PC descriptors. That might reduce the amount of (what The Forge has called) "pawn stance" play - ie action declarations that are nakedly motivated by the player's evaluation of the situation, without any attempt to establish an in-character rationale - but I don't see it going much further than that.I think that arguing that it needs a DM to work is a fairly weak criticism.
I never made any claim that 5e is the ideal game for running a narratively focused game. I said that it was capable of running either a narratively focused game or an old school dungeon crawl.
As for the rest of the system for non-combat resolution, it seems to me to be relatively weak as far as player control over the shared fiction is concerned. There are spells, as has been discussed, but not much else. A player can say what his/her PC tries to do, and that's about it: there is no framework for establishing binding stakes and consequences, for instance.
The idea of RPGing-as-storytelling-by-the-GM has a long history, going back at least to the early 1980s (the DL modules are an early published example in D&D; CoC exists around the same time and is perhaps an even clearer example of the same sort of approach). 5e's non-combat mechanics are quite well-suited to that, because (as I said just above) they don't generate significant constraints on the shared fiction.I haven't watched the show in over a year, but I can recall quite a number of times when one of the players suggested doing something extremely non-standard and Mercer rolling with it. Like a spell that wasn't in any way meant to do X, but flavorwise could hypothetically do X, doing X. Sometimes I think there might have been a check involved, but I don't recall with certainty.
Moreover, the game has a strong narrative focus. There's a story there. While some of it is emergent, a lot of it is clearly planned, and planned with the intent of telling an entertaining narrative.
And the players have no other way to introduce significant constraints on the shared fiction.
Which means that the GM is largely free to introduce whatever s/he wants to into the shared fiction, ie is largely free to tell a pre-planned story.
So best practice advice for playing 5e would probably begin from a recognition of these points, and then advising GMs where to go from there.
I saw this evidenced recently, when my daughter played her first D&D game with friends over the school holidays. The GM clearly didn't have a pre-planned story ready to go, and the result was aimless, structureless and ultimately (for my daughter, at least) disappointing play. And her experience drove home (to me, if not to her - she doesn't think as much as I do about RPG design) the lack of levers that 5e D&D players have to drive things forward or actually make the fiction develop. All they can do is wait for the GM to tell them things.