How about The Legend of Zelda for Wii, which was on GameCube?

Probably the  bunch of GBA ports that were released over a decade ago. You know, because thats relevant to the discussion...somehow

...or worse: Every Nintendo game ever is a rehash of the one that came before

Twilight Princess?

Released the same day. 

Yeah, that's the one. Came out early in the Wii's life.

They were released on the same exact day...

Correction: Wii launched first.

They promised Twilight Princess as a GameCube game, but delayed it because the game needed more time in the oven and to have a good launch title for the Wii.

The GameCube version launched 3 weeks after the Wii version in NA and 1 week later in the EU, it was meant as a nice gesture (because they wanted to keep their promise to release it on the GC).

Thats by no means a cash grab or a "rehash" .

But why would you have it on the Wii if it's on the GameCube already? And it's not even at a later date!

That one was a Wii launch title and released only a few weeks after the Gamecube version. It was a cross-gen titles, yes, but not exactly a re-release.

Edit:

Got it backwards. The Gamecube version was released after the Wii version.

It wasn't on the Gamecube already... it was on the Wii first, and released on the gamecube later for people who had been expecting it on the GC as that was the platform it was initially announced for.