The GameCube was always going to "fail" in the sense that Nintendo (very optimistically) expected that they could take the console throne back from Sony and the PS2, or at least seriously compete for it SNES/Genesis-style, in the console's first year. That was never even close to happening.
But when it failed to to that, Iwata called it a failure and began to shut things down. And that caused the GameCube to fail even harder and allowed Microsoft to surpass them with the XBox, a mistake which Iwata himself even recently admitted and said that he learned from when the 3DS was in trouble.
Iwata's new direction that he charted with Wii included the philosophy "We will never win against our hardware competitors on even terms, so why bother wasting energy trying?" And he was celebrated for that. But that retroactively added another level of failure to the GameCube. The GameCube tried to compete, and according to Iwata, it wasted it's time. And anyone who believed in the GameCube was a fool for doing so, because Iwata didn't follow though, which means that next time Nintendo asks us to believe in their commitment to hardware, we won't, because we've heard that lie before.
The GameCube was a fantastic piece of hardware. It was better and more dev-friendly than the PS2, on par with the Xbox, and profitable at 2/3 the price of either console, both of which were losing serious money.
And waggle was a GameCube innovation. It was being shown to GameCube devs (in an unfinished state) even before the GameCube launch. When Iwata saw that the GameCube was a failure, he took everything that was good about the GameCube and relaunched with a new name. If Nintendo had produced a "GameCube 2" instead of a "GameCube Turbo", with all the strength shown in the GameCube's design, people would have still been lining up around the block at E3 for a chance to experience waggle for the first time. It wasn't Wii's lack of 720p that drew people to the system, and it sure wasn't Nintendo's profit margin, which vastly exceeded the N64 and GameCube's profit margins.
Sony fell on their face with the PS3. And Microsoft's biggest advantage was their one-year head start. Howard Lincoln learned from the SNES and told the world (as mentioned in this article) that being first to market was meaningless. Because the industry would wait for Nintendo. That sort of happened with the N64. That did not happen at all with the PS2/GameCube. And that one year head start is what made it utterly impossible for the GameCube to catch the PS2. Iwata identified this as arrogance and vowed that he would launch first in the next gen. And then MS to beat them to market with the 360. And then he dismissed that second blindness regarding Microsoft, claiming that MS wasn't a real competitor, only Sony was. And yet, the 360's head start gave that upstart MS the lead against Sony for several years.
I would maintain that if Nintendo had launched a 720p-capable dev-friendly and profitable GameCube 2, before or around the time of the 360's launch, powered up with the immense demand we have seen for waggle, the videogame industry would have been revolutionized (as opposed to being fractured between casual and hardcore), Nintendo would have been the lead console, Microsoft would have nearly fallen off the map, and Sony would have remained an expensive but needless alternative. Nintendo would have won our current generation of consoles, their third party relations would be repaired, and they would be the hands-down favorite to win next gen.
But instead, they made mad bank for a few years, and now they're paying for it.