The idea that what we're calling the fiction is 'just flavour' is probably a core problem in how different people see what playing an RPG means.
When I'm reflecting on RPGing, I find it helpful to distinguish between
mere colour/flavour, and fiction that actually
matters to the play of the game.
Eg in dungeon-crawling D&D, the colour of the NPC's trousers normally is mere colour; whereas the location of the door in the wall, or the position of the chest in the room, is not: architecture and (at least some) furnishings are the stuff of which dungeon-crawling D&D is made.
When I play Prince Valiant, the location of a door in the wall, or the position of a chest, will typically be mere colour. To the extent that clothing can signal social class, it will probably be more important, as fiction, than it is in classic D&D.
Upthread, you talked about His Majesty the Worm, where the role of Bonds means that relationships between PCs become more than mere colour. The same is true in my Torchbearer 2e game, where the bickering between the Dwarf and the Elves isn't
just "for fun", but also plays out - or sometimes plays against - Beliefs and Creeds and so is part of what drives the core engine of play.
I also see this as closely related to this from upthread:
Nothing that has stakes and requires resolution is actually being resolved, so we're in thespian "acting like my character and having conversations" mode. Which I know plenty of players who want that to be like 95% of their gameplay, but isn't really the intent of Blades.
I tend to prefer
stakes to no-stakes. (Which doesn't preclude acting in character and having conversations. It's only if one assumes a traditional D&D resolution system that such an inference would arise.)
I think 4e probably was a notch further along on this than older editions, but only one notch. The unforgivable crime that 4e committed was just being honest and clear about it.
I did not find 4e D&D to be lacking in colour that mattered. I mean, that's obvious for skill challenges - actions can only be declared once fictional positioning is clear, and the resolution of each action changes the fiction and hence the decision-space for the next player and their character.
In combat, of course there is some stuff that 4e is indifferent too - eg whether a blow strikes the arm or the leg - but in that respect it's no different from other versions of D&D. But I've never had a similar experience of gonzo fantasy action in another FRPG. From using cold magic to freeze puddles into ice (Icy Terrain), to blasting demons through upper-storey walls into the street below (Thunder Wave), to pursuing goblin archers and cutting them down before they can escape down a secret hatch (Mighty Sprint + Come and Get It).
I know there were some would-be 4e players whose whole experience with the system consisted in being confused by their knocking of snakes and oozes prone. Thankfully for me, I wasn't one of them!