If that were true, Jagar Tharn would still rule the Empire by the time of Oblivion. And then there is the whole thing about Dagoth Ur taking over and the inevitable rule of Mehrunes Dagon. That's not whats happens, isn't it?

Yes, everything ends and blood will always be spilled in the Arena, but never before was a hero denied their place. They always fought against overwhelming odds and pushed back being far more powerful than they were.

The Champion of Arena didn't die in the Imperial City while Tharn continued his rule, Silmane and the Hero stopped Tharn. That doesn't mean everyone lived happily ever after, but Tharn, at least, was stopped.

The Nerevarine didn't fail or didn't manage to stop Dagoth Ur just to die while the temple/some random person who happened to be nearby claimed the victory for itself.

The Hero of Kvatch was just a helping hand in the Oblivion Crisis, but a fate-defying hero in Shivering Isles. By saying "Nope, they just are another pawn in the daedric game", their deeds are just thrown away and that hasn't happened before. And TES wasn't just about how "everything sucks but you get to do cool shit".

The Sheogorath-situation was left ambiguous for a reason. Did the hero become Sheogorath? Did they just rule the isles until a new one appeared? Did something else happen?