It's not like Nintendo has a very positive connotation anymore. At its best, it's still sometimes synonomous with videogames, but merely the idea of a videogame, not anything necessarily specific. Nintendo remaking their brand was the smartest thing they did with the Wii outside of the controller. I think Nintendo's chances to ever be seen as cool died the moment Halo was released. People wondered how Nintendo would ever recover their image. Well, they sidestepped it, essentially trying to stop pleasing the very consumers who had written them off to begin with. I say Halo was a turning point because with Goldeneye and Perfect Dark and a smattering of decent sports and racing games on top of their already robust first party lineup, Nintendo still was at least somewhat relevant in America. That ship sailed when the GC was released.
Incidentally, I think the Wii was the perfect storm. Without the embarrassment of the GC, without the technology, without the transformation of the Japanese market, without the issues of Sony and Microsoft, without the DS, would they be where they are right now? Sony did something similar in a dissimilar fashion with the Playstation. Throwing another reference to Apple, the iPod brand has become its own thing. I think Nintendo could have energized the brand had they chosen to. Essentially, it comes down to the controller. But the Wii names helps so much with branding purposes, and of course it's basically its own clean slate: they can mold it however they want based on the perception they're hoping to acquire. It's not just the system, it's not just the controller, it's an instantly recognizable face that everybody will identify. I think the Nintendo name itself has benefited greatly because of this, and I can still see them using it, and now it is actually relevant once again.
EDIT: I think Parl is being sarcastic. Then again, you can never be too sure on GAF.