First of all, the GameCube did not have good third party support. It got better multiplatform support than the Nintendo 64 did but didn't get nearly as many exclusive third party games as the N64. Not to mention, third party support for the GameCube pretty much collapsed after mid-2003 whereas the N64 continued getting third party support throughout most of it's lifetime.
That being said, both Wii and Wii U pretty much built on what the GameCube was. The problem is the power wasn't there. Technology is part of the issue. Could Nintendo have released a $200-$250 console in 2006 that was on par with Xbox 360 and PS3? I don't think they could have. The Wii U is expensive because of the Gamepad, but even if there were not Gamepad, what could Nintendo have done to make it cheaper. With GameCube, the right technology was available at the right time. In fact, pretty much everything about GameCube was done right. The only problems were that they couldn't market it to an older audience, it looked too much like a kid's toy, and Nintendo would not commit to online.
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