BitD has scene setting processes that outright demand explicit negotiation. For example, the Devil's Bargain.
Picture a player continually explicitly negotiating every Ability Check modifier set by their referee in OSE. In common approaches to play that could well feel disruptive. It's not demanded or advocated as part of following those rules, under which players enjoy a flow of play facilitated by tacit agreements in place up front. That doesn't mean there is never a moment of overt negotiation, nor does it deny that agreements are implicit in every act of play.
I agree that modern RPG designers are generally aware of the relationship of rules to agreements, without that meaning they always design for overt moment-to-moment negotiation. They're also aware of what they can achieve by making erstwhile unspoken up-front agreements, spoken.
I think each game design is unique in its approach to this. In PbtA games (of my familiarity, I'm sure there are variations) there isn't anything like 'negotiating a DC' at all! I mean, you could dispute with the GM as to which/any move has been triggered, though I don't see that a lot. Now and then a player might say "but maybe this other approach makes sense?" and I'm OK with calling that 'negotiation', but I haven't found it super prevalent in DW or Stonetop. It's more likely that negotiation in DW will happen in terms of what the fiction implies and 'how things are', which then indirectly leads to 'and then which moves will happen.' So, I don't think in my PbtA play I would normally see every check being negotiated.
OTOH in BitD the negotiation point is much more on the 'what fiction will arise from picking THIS ability vs THAT ability', though again I think the negotiating is much more centered on what fiction is going to arise, or what does the current fictional position impose in terms of 'blockers' or obstacles than on 'DCs' (in BitD that would be position and effect mostly, though it could also speak to how you can resist, etc.).
In both games a central nexus of negotiation, however, is "what generally is in the fiction?" It's narrower in BitD because Doskvol is a very nailed down environment in general terms. The possible things that can appear in Doskvol is limitless, but they will all clearly fall into its genre conventions, which are pretty strong. DW OTOH, or even more so AW, is less nailed down in this sense. You could have almost anything materialize as a threat in AW, space aliens, AI, zombies, grey goo, Saberhagian sentient atomic explosions, the sky is the limit there. The point being, the exact scope of that negotiation is, again, game specific, but the focus on overall high level goals and direction set by players is pretty consistent.
So, yes, and this is a point that is germane to the 'feel like you matter' thread, having such mechanisms as part of the game is highly significant! OSR type play doesn't have them, and thus attempting such is highly awkward. Its also an agenda bender I would say. There's nothing wrong with non-narrativist play, but it does distribute power differently at the table by virtue of NOT having certain types of rules. While this was simply happenstance in the 'old days' of '70s and early '80s D&D it is certainly very deliberate avoidance today.