I'm not too sure about the hero of Daggerfall, but the Nerevarine and the Champion of Cyrodiil didn't neccessarily leave Tamriel.
Nerevarine - Since when where rumours the 100% accurate truth?
CoC - Didn't neccessarily become Sheogorath. Each hero only does the main quest. The Nerevarine wasn't neccessarily the Arch Magister of Telvanni, for example.
I may be wrong, it's just a brain fart I had. :shrug:
Nevarine leaving for Akavir explains why St Jiub is the one stealing headlines fighting Daedra in Morrowind during the invasion and not the Nevarine. I see what you're saying, but the Shivering Isles is an expansion, not a side quest like joining fanctions. It affects Oblivion and Mundus since it pertains to the sphere of Madness.
Joining the Telvanni doesn't affect what the Morrowind PC eventually becomes i.e. Nevarine, Blodskaal etc. Just the same way joining any fanction has no bearing on the Oblivion PC becoming the Champion of the Cyrodil, Divine Crusader or Sheogorath. A sidequest only colors the PC's background/story, a main quest (Shivering Isles expansion) defines what he becomes.