Most of the good GMs I've been around have written up things because they wanted the players to find out about them.
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In my instance, I enjoy being asked specific questions about my setting--I have a number to answer before a session tomorrow night, and I'm expecting to have a good deal of fun doing so; but the questions are relevant to PC goals, so very much in service of PCs' dramatics needs, IMO.
I think this is an example where we can probably talk meaningfully about the point of the GM's notes, how they contribute to play, and how player's learning what they say factors into that.
Of the past four sessions of Clasic Traveller that I GMed, two of them had a large component of the players discovering the GM's notes: the PCs were escavating and exploring an ancient pyramid complex buried under 4 km of ice. Some of the play was focsed on the action declarations that would put the PCs in the fictional position that would enable their players to declare the actions that would trigger my exposition. I had deliberately set it up so that those action declarations woldn't be "puzzle solving" (as in
how do we excavate 4 km of ice) but rather social dynamics: there was a group of NPCs at the site, with drilling and blasting equipment,
and the PCs had a starship with a triple beam laser that is prety deadly even over 100s of thousands of km in space, so the immediate situation was about how to resolve rival claims to the site and how to integrate (or not) the efforts of the two expeditions.
Once the PCs entered the complex, I narrated away, referring to my notes (ie Shadows in Double Advntre 1) and making appropriate adjustments on the fly to bring the ficational elemements into line with my conception of the place which was built on what had already been established about these aliens (which was different from some of the premises of the module).
In the last two sessions, the "exploration" aspect has dropped away a bit, which I have found good. The old Traveller modules are not terribly dynamic situations as written.
If the intended purpose of play is to change the setting, there needs to be some definition of what the setting is before the change.
This is an interesting point, but I don't think I agree with it. At least not fully.
For the players to self-consciously change the setting there does need to be some shared conception of what the setting is. But I don't think that requires the sort of GM-side prep work that I (at least - maybe others would agree with me) would associate with a sandbox.
Dogs in the Vineyard, for instance, includes changing the setting as part of the goal of play. But it's approach to setting is very different from what (say)
@Emerikol is describing in this thread.