On the one hand, Vincent Baker is obviously a genius of RPG design. On the other hand, he didn't invent AW from whole cloth. The idea that players might help establish setting and context for their PCs didn't begin with AW, although there's no doubt that AW takes a big step in the way it tries to systematise and articulate the idea.success with consequences is baked in. You certainly can play D&D in a similar fashion, you do and I do for example, but it's not baked in in quite the same way. So while it's true that "there is nothing about D&D that has to get in the way of that", I would also submit that there is very little that actively encourages it either.
I'm also not strictly talking about moves when I'm talking about the allocation of narrative responsibility either. Right in the original AW game rules the suggestion is made that the players should be regularly responsible for the description of things, and that the specifically that GM use the players as a resource in this way. That is really not the case for D&D.
For instance, Classic Traveller 1977 (Book 3) says that
At times, the referee (or the players) will find combinations of features which may seem contradictory or unreasonable. Common sense should rule in such cases; either the players or referee will generate a rationale which explains the situation, or an alternative description should be made.
When my group started our current Classic Traveller campaign, it was one of the players who suggested that the starting world, which I (as referee) had rolled up, was a gas giant moon.
So from my point of view, it's not so much what D&D actively encourages, but rather what is about either D&D rules or D&D culture that actively discourages players engaging with the fiction in that sort of way? (And it's not like D&D is a monolith in this respect. There's 4e and especially but not only the DMG2 - eg the idea of player-authored quests is right there in the PHB and DMG. And as I said, I was working out some of this stuff for myself around 1986/7, GMing AD&D.)