I think you just described why I find a lot of tragic events in fiction (not just deaths) not very impactful. When bad things happen to characters, my brain registers they're in a bad situation and if it's particularly awful I'd feel horrified and nauseated, but not really sad when it's just an event that could happen to anyone.
To actually touch my cold, dead heart, it has to have been something that could only have happened to that particular character because of who they are and what they did as an the particular individual they are.
For instance, let's say a princess has a very strict upbringing where she must be perfect and isn't allowed to make any mistakes or else she'll face severe punishments. Ouch, but also ... kind of ... whatever? But let's say her parents weren't that hard on her before, and everything was totally fine in her life, but one day she learnt her parents are corrupt and treating their subjects unjustly and she calls them out on it, which causes them to put their foot down and keep her on a tight leash so she doesn't step out of line and threaten their power. That's the kind of stuff that'll actually get me empathizing with a character rather than just sympathizing on a cognitive level.
Huh, I read the OP as basically this in spirit - that for a character death to be earned, it has to be causally connected to the rest of the narrative somehow. Do you feel like character deaths that aren't connected to other things via causal transitions can be nevertheless satisfying or worthwhile?
Personally I do agree that sometimes deaths that come out of nowhere can be worthwhile, but only if it leads to future events that could not have happened without that death happening the way it did. If not causally connected to the past, it needs to be causally connected to the future. Have people mourn the death, or reflect on their outlook on life, or use the death to further their plans somehow. But if the death came out of nowhere and the response to it is 'oh, they're dead, guess that's resolved then, time to move on like nothing happened :D', then I think that's pretty unsatisfying :'D