Well, it depends on the game and playstyle. Some TTRPGs have very little difference between GM and player. So again, why does there need to be strict control placed on the frequency or gravity of player worldbuilding vs GM worldbuilding? As an example, the so-called 4D playstyle proponents use a technique called "co-creation" which essentially allows players completely unrestricted worldbuilding permissions, independent of system used.
Burning Wheel is purpose built for player driven campaigns, so it's assumed that there are no predetermined plot points for the players to experience. The game also leans heavily on the collaborative aspects of play so the GM would be expected to alter things to conform to the new lore the player has added. While it doesn't explicitly say so, I believe Burning Wheel was created as a response to an overbearing and controlling GM style of running games.
I've watched a great many AP vidoes over the last few months, and I don't think a single GM controlling the lore means things will be any more coherent than if the players can also create lore. In my own personal experience, I know it doesn't.
Again, what it really comes down to is trust, and not just trust in process, but trust in the participants to collaborate to create a fun and interesting experience for all. As a player the default position regarding worldbuilding is to trust the GM implicitly. All this particular methodology asks is that the GM trusts the players in the same fashion.