Nintendo probably in third place

Let's face it – the GameCube didn't exactly have stellar third-party support. Other than the usual first-party Nintendo games that most people purchase Nintendo platforms for, there was nothing on the GameCube that screamed “buy me.” The PS2 had everything and Microsoft's relatively new Xbox was gaining support quickly. Nintendo knew it had to do something to really shake up the market if they ever wanted to get back to their “glory days” of the Super Nintendo. 

Launching a GameCube 2 with hardware specs comparable to the Xbox 360 might have seemed like a “safe” move for Nintendo, but in reality there would be nothing safe about that. A GameCube 2 would have been far more expensive to R&D and manufacture for the company, and the mindshare over the past several years was clearly in favor of Sony and Microsoft. The odds are Nintendo would have spent even more money on GameCube 2, still launched a year after Xbox 360, and the results probably wouldn't have been much better than GameCube.  

People sometimes act like Nintendo is this altruistic entity that is trying to do good for the entire video game industry, but let's not forget that they are first and foremost a corporation and will do whatever it takes to profit. After a careful examination of the industry and their place in it, Nintendo's key decision makers figured out that in order to regain the upper hand they'd have to go in a radically different direction and disrupt the marketplace. It was a truly brilliant business move.