Man, some incredibly awesome RPG systems don't even have rules at all for resolving actions that the PCs aren't involved in!
YMMV. Those same games would be unplayable to me.
I've been thinking about this response, and there is a playstyle difference that I find quite interesting here. This might be long winded, but there's a point eventually.
When I sit down to play a role playing game with other people, when the rubber hits the road so to speak, what I really care about is running an enjoyable game for the players, getting to the action (whether that be playacting or murderhoboing), and creating an exciting play experience.
One of those things that is important is player telegraphs, and one way you can read players is by looking at their character sheets. For example, if the ranger took Favored Enemy: Elephants then it's likely he's looking to be a big game hunter. If the rogue has lots of social skills, then he's looking for some intrigue. Likewise, a player who took the Lightfoot Halfling race wants to play a sneaky little guy who can hide really well. I want to give them that! I can use that to my advantage and give them lots of opportunities to sneak and hide, and if he wants to do that in combat, because that's what his race
does then I am more than happy to go with it.
Second point is that, for me, the rules as I see them exist so that when a player wants their PC to do something that is risky, we have a common framework to see if that thing is successful. They aren't there to make DMing decisions for me or to constrain events that occur without PC interaction. When a PC isn't involved with something, then its just the DM playing with himself. It isn't until the PCs get involved in the action that the DM is playing with the payers. And, even then, everything outside the scope of the players' own actions are things that they're observing and that need not be influenced by randomness.
If an old man is trying to sneak past a goblin, and neither is a player's character, then I don't see why it would matter to the players or the DM whether the result of that action was resolved randomly or by fiat. I suppose you could try to claim that if the PCs have a vested interest in the survival of the NPC that the DM can use randomness, find that the NPC died, and then claim neutrality. But, then, my assumption is always that the DM and players interact upon the world in good faith. If the DM is operating in good faith, then he has no need to relinquish responsibility for actions that take place in the game. A DM who takes ownership of what is happening, I would think, would be much more even handed, thoughtful, and less capricious in their approach to events outside the PCs' control. In fact, they often lead the DM to involve players in those scenarios more often, leading to even more player agency.
So, then back to my original thought about what is important in the game at the table. I find the desire to pare down PC abilities (re: lightfooted halfling) while simultaneously focusing on the resolution of NPC actions as important to be somewhat the reverse of what is the focus at my table. For me and my games, the player is the important thing, not the NPC or the world or anything like that. Beyond the player everything else is secondary. I want rules that give the players lots of agency, and I think it is important to run a game with an eye toward giving the player abilities lots of spotlight and fun. NPCs are important to me so long as they are important to the players, and rules for them I can take or leave, whatever fits the situation.
This isn't to say that my way is right, of course. My thoughts are cultivated on the games I like best. And those games tend not to be Dungeons and Dragons nowadays. As my tastes have wandered to things like Fiasco, *World, FATE, and Dread I've changed my idea of what makes a good game considerably. I expect them to continue to change. It's discussion like this that help me analyze my thought process and help that process along.