Is your assumption that players will withhold from asserting anything within GM's purview? GM won't need to say "no" because players self-regulate. You then might be saying something like
what players say their PCs attempt will be added to the fiction unless it invokes a game mechanic
It doesn't add anything to this for GM to say "yes", but a necessary job
someone has to do is say whether what's said invokes a mechanic.
I'm finding this aspect of what you're saying elusive. Given GM must say "yes" what holds up what player said from working when no game mechanic applies? It seems there must something more going on... perhaps another layer of player self-regulation?
I don't think so either: it's more "say yes OR roll to find out". That aside, it does seem to me that your envisioned style of play requires players to withhold from saying certain things. Meaning the approach becomes something like
players self-regulate what they say, generally* limiting themselves to saying only what their characters attempt
as to things players permit themselves to say, GM says "yes" or invokes a game mechanic
Suppose a careless player intrudes into narrative space they aren't supposed to have any authorial control over? Does GM say "no" in that case? If not, what work is "yes" doing here?
*I added "generally" here to echo your wording in the quote at top, but doing so makes the meaning ambiguous. What are those other sorts of things players can say that aren't "what they have their PCs attempt"? Where do the boundaries of that lie? A parsimonious approach would eliminate "generally".