I'm just going to ask, being somewhat naive in this...
(1) Why are the specific rules important when you're working with stuff that's more or less off-screen?
Because Game Master is a fallible human being - the rules somehow mitigate this by limiting the scope of his imagination. Ensuring believability of offscreen changes is one of key rules for me - and I strive to achieve that in such a way that every creature, be it a PC or NPC, works in the same way.
(2) While I understand that the "world" exists when everyone is sitting down and playing D&D, I don't understand how it exists when you're not playing D&D. At least, it's no more existing then, than it is for a novel-writer.
Players have characters to roleplay. I have the whole world for the same purpose. They use xp to advance their fighters and mages, while I use their actions to advance my setting while following side stories of NPCs.
It's handy to look at statblock of NPC brother to PC priestess and find out how he is doing during archeological expedition he is managing. His statblock tells me what I can expect of him and limits the results of his action to believable frame (he is out of his depth trying to deal with natives - his interpersonal skills may be decent, but his elven heritage prevents him from fully acknowledging his local partners as fully trustworthy allies - or, in game terms, he may have some Diplomacy ranks, but average Charisma and racial prejudices led him to somewhat aloof attitude... which does not help to make progress).
Meanwhile, sister of the ambassador is racing against time to save her brother since, unknowable to him (and partly to her - well, he knows and he suspects but tries not to worry her) he is suffering from slow degradation of his vessel (body) due to incompleteness of the process involved in the restoration of his health in his youth. Again, her stats determine her chances of success and again, they limit my imagination (i.e. prevent the use of Deus Ex Machina).
What is going to happen to those two NPCs? Will they succeed? Will they fail? Time will tell, and their paths finally cross the paths of the party, they will have long stories to tell.
Novel writers don't, generally, need RPG rules. Why should a game world need RPG rules during times in which you're not using it to play a game?
Ah, but I do play. It's just that it is not as detailed as RPG session. It's a roll-a-week, look at the stats and then think what would they do and how they would react given the development.
Right now I have several key NPCs, each one of them controls portion of game world and, by actions of such NPCs the rest the world progresses. Their progress is tracked by gazetteers I write from time to time to record changes.
Finally, I am also, using two-three random tables, add completely random stuff (like a minor tectonic tremor, outbreak of small-scale disease, particularly successful crops) to further breath more life into the world.
It is not much work but it requires consistency and consequence. That's why unified system works best for me (and why Profession and Craft skills are a boon to me).
Regards,
Ruemere