Gamecube came 'last' because of three things. 1) The PS2 2) Coming out after its biggest competitor and 3) No third party support (also the PS2).
Frankly, its can be seen as partially a fluke that the Wii didn't suffer the same fate. Or Nintendo purely forcing the Wii not to suffer the same fate and doing something so bold, it couldn't fail. But as it is, the Wii has two of the three problems the Wii does. Little third party support and it coming out after a major competitor. Just, this time, its not trying to directly compete with its competitors in things like graphics and 'mature' games like the GameCube was. Its doing the exact opposite. And that, along with the total lack of third party support, was the major problem with the GameCube.
There's also little things. Like the GameCube had big spaces in between major game releases (not unlike the Wii) and the system didn't have a DVD player. But these things aren't as big as the main three issues. And didn't cripple other systems which had the same issues.











