A funerary procession like in Daggerfall could fit, i suppose, but anything beyond that could be problematic. For one, look at all the people who gripe about Skyrim's main quest being too forced, and having too much significance? What do you think the reaction would be if every time you died, you saw a scene of Alduin consuming the world? Or of Dagon's armies burning their way across Tamriel? Or of a world populated only by 6th House abominations?
Any other option would require special mention of guilds, organizations and people, with a lot of tracking. Imagine you become the leader of the Companions... The 'ending' you get when you die now mentions you rebuilding the companions into a prosperous organization, renowned across Skyrim and beyond. Your wife Aela mourns your passing. Except, oops, you didn't marry her, and she died on a hunting trip as your companion. Farkas takes your place as Harbinger... oh wait, he was eaten by a dragon on that one dungeon run.
See the problem? In order to add character and relevance to it, you need specifics, and well... those can become complicated to track. Otherwise, you simply get foot-notes which are irrelevant to your particular playstyle or character.
There may be a happy medium between too specific and too generic, but really... What would be the point? Regardless of how people play, TES games aren't about dying and the legacy you leave, they are about living a life, adventuring and interacting with the world. In essence, they are about DOING, rather than DONE.
If, in the future, we have a TES game which is about surviving as long as possible, or having a personal impact on the world (think splinter timelines) then maybe these types of personalized endings would be appropriate. But until then, the only impact dying has is
A; Before you defeat the big bad, dying means failure and the end of the world
B; After you defeat the big bad, but before completing DLC, dying means the end of the world through secondary means
C; After you defeat the big bad, and all the DLC bads, dying means disappearing from history
In the first two cases, we're back to the first point. If you just want to play a Bandit, do you want to be reminded that Alduin's trying to destroy the world every time you die? In the last case... What's the point? You'll find out your legacy in the next game.
Which, i suppose, could be a bit of an interesting inclusion, giving some prelude to what will be history by the time you pick up your next TES. Still, does anyone thing Bethesda is thinking that far ahead?