The Fantasy Mesoamerica in my setting isn't even really informing anything the PCs are interacting with, though. I mean, it's (at least mostly) where coffee, chocolate, and vanilla come from, but that's about the extent of it.Right, because it informs other components that the PCs will interact with. Like you can't run an Age of Sail campaign without knowing how colonialism informs European society even if you don't actually want to play colonialism. That makes sense.
What I mean when I say improv elements necessarily lack depth on introduction is that improv is like live development without the benefit of being able to.throw out the dross that always come with development. If you create a NPC in play, they are necessarily lightly sketched (aka lacking depth) at first. If the PCs immediately pursue more information at the moment, you have to make up additional details, adding depth, but you are likely to be stuck with some details that, being the first thing you thought of, might not be great. If, however, the players plan on meeting again with that NPC in a later session, you have the opportunity to add depth with the benefit of muling things over, thinking things through, talking to a fellow GM, looking back in your notes in order to better tie the character to established lore, etc.
The improvisations I make are often constrained or informed by previously established things in the setting. I have at times made decisions after introduction that ... changed the lighting on them, at least.