I think there are a lot more of these moments than we suspect, if only because there are many locations like the Jarls' palaces that we tend to visit only when we have business there. Get in, take care of business, get out. If you hang around an otherwise busy place long enough and often enough you see NPCs doing stuff that you never knew they did if the only time you paid attention to them was when you were looking them up to do some bartering or advance a quest.
I spent a lot of time in the Palace in Windhelm at the end of my last character's career, because I was playing around with a lot of mods for Ulfric that resulted in me marrying him and having him as a follower and there were conflicts so I was around there for days of in-game time taking mods in and out and trying to figure out what worked and what didn't. He would go missing sometimes and I'd be all over the place looking for him.
Nothing remarkable, really, but during that time I went into the "map room" off of the main hall and found Wuunferth, the court mage, standing over the table where Ulfric normally stands, peering down at the map. Another time I found him sleeping on Jorleif's bedroll in the kitchen, which was really odd since he has his own room and bed (which was empty at the time). Up until then I had never seen him anywhere except in his own room, just sitting there or at one of his crafting tables (or sleeping in his own bed). But apparently he actually does roam around the palace and do other stuff, I was just never there often enough to see it.
It's cool to think that guards and citizens in Whiterun are also stopping by Farengar's rooms to enchant stuff. I once found Amren sitting upstairs on one of the benches in the "Jarl's quarters" section of the Palace - no idea why he was there, maybe he was just killing time until the enchanter was free.

But it does give that feeling that not *every* party waits on the Dovahkiin's arrival to get rolling, which is nice because there's enough of that in the game already.