Perhaps, then, this is the issue.
I see a death caused by the dice--a death that just happened, with no context, no resolution, broken stories that will never ever get anything more than an "oh, yeah I guess that happened" is the antithesis of interesting to me. It's saying you should get super duper ultra invested in a story you KNOW will only get half-told, and then peter out into nothing.
Whereas it seems like, for you, the point here is exploring a "narrative interruptus." I just...don't actually see that happen with characters who die due to Random Kobold #6 getting a crit or Stupidly Bad Luck Climbing A Steep Cliff. I don't see players asking questions like, "What happens now? How do people grieve? Can we move on? Should we?" I see Pam VII, Second Cousin Twice Removed of Pam VI. Or I see (as mentioned upthread) that some random mercenary just joins up with the party out of nowhere, and almost instantly slips back into the same camaraderie and presence in the group.
There is almost never an actual period of mourning, of falling into weird coping mechanisms, of genuinely asking what one is going to do. There's no vengeance to swear against, because the source was something so mundane and dull it doesn't merit such a thing, it's just the world being a sucky place. Maybe you try to take up a quest or goal of the dead character, but such an "I am Spartacus" response is effectively a denial of the original death anyway (the dead character so, so easily becomes a Flanderized subset of the character that takes up the quest.)
Would you agree? It very much seems to me that there's this baked-in assumption that everyone becomes deeply introspective and demonstrates a nuanced and thorough-going investigation of the loss and resulting difficulty etc. and...I just don't see that assumption play out. Players move on way too quickly because three weeks out from the death, you have more pertinent concerns, and the gap between player feelings and character feelings makes grief not very interesting.
And the only way I've found to actually get that sort of introspection and nuance and investigation is to talk about this sort of thing in advance. To get people on board with the story, thinking about the directions it could go, etc. Which is only the tiniest bit different from, y'know, just handling the death differently. E.g. you can still get all those delicious "how do we move on, should we move on" etc. questions by having a lengthy quest to save the dead character from their fate, which can have a huge list of negative consequences all on its own.