An RPG system exists to objectively describe things, including all of the characters, for the purposes of impartial resolution.
Well, that's a highly contentious claim. It's not one that I accept. It's certainly not universal, nor even especially widespread, among RPG designers. It wasn't accepted by Gygax, who was one of the inventors of the game-form (he tended to accept the impartiality idea, but not the "objective description" one - see eg his discussions of hp, saving throws, XP and combat resolution in his DMG).
The point of mechanics is to make playing the game an enjoyable experience
I guess that's true, but it doesn't really tell us
how they do that.
The rules aid GM adjudication.
That's a very Gygax/Moldvay take!
I incline towards Vincent Baker's take. RPGs are talking games, in which - by talking - participants introduce new content into the shared fiction. Sometimes there is disagreement or uncertainty over what content to introduce into the fiction (the player wants it to be that his/her PC killed the orc; the GM thinks there's at least a chance that it's the other way round). The mechanics resolve these disagreements and uncertainties.
As DM, you are the laws of nature, impartial adjudicator of all things. You have no objectives
I think you intended the "you" in these sentences as impersonal, but if so then the sentence is false. Because I am a GM and I am not (only, perhaps even typically) an impartial adjudicator, and I do have objectives.
Treat the world like a living world. Place NPCs and monsters where they make sense, based on how the world works, rather than what you think would make for fun encounters based on the party or their levels.
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Any conflict or drama that happens around the PCs ("on-screen") is just a byproduct of your honest presentation of the world, the characters, and their goals.
I don't understand what constraint you think the last sentence imposes.
The drama in which Tolkien's hobbits find themselves enmeshed is a result of the world, including the world of characters and their goals, in which those hobbits find themselves. But from the point of view of crafting the story it's hardly a coincidence that those characters had those goals, or that the events unfolded just as they did.
If I think it would be fun for the PCs to meet the tarrasque (and I do) then I can trivially come up with a reason why they might (I did, over the weekend - it will also involve Maruts observing affairs somewhat like the Celestials in Marvel Comics, only less massive). I am honestly presenting the world - but the content of that world wasn't drawn out of a barrel with my eyes shut!