It seems the solution in many people's minds is to basically wash Nintendo out and make them "a western company". In a sense, if that happens I think many people should get their wish and Nintendo should just go third party, software-only. Because by that point, it'd make no difference. Nintendo wouldn't really be Nintendo anymore.
I believe there is a perspective gap in which it is simply not understood that the "Nintendo magic" imagined to be greedily hoarded for Japanese centric operations and so-called "Japanese style games" is a holistic creation of the Japanese centric operation and so-called Japanese style games. This is what Nintendo is geared for. Some of the calls for Nintendo to change everything about themselves make as much sense as people suddenly and arbitrarily getting on a bandwagon to demand Blizzard stop everything they do and make fighting games designed to be released in Japanese arcades.
That said, while Iwata is regarded as a cartoon villain who doesn't want people to have games because he's a mean man, Nintendo's real troubles started long ago. Before Iwata. Anyone who steps into the hot seat at Nintendo has a big problem on their hands. Nintendo "lost" the game as many seem to perceive it, with the N64. They lost mainstream 3rd party support. It's unknowable whether or not there was anything they could have done to totally blunt Sony's advance, but rejecting CD media lost them momentum in the direction the industry was going. Ever since then, Nintendo has been trying to find a place for themselves, IMO. With the rise of Microsoft in console gaming, there is not a lot of gap left for a 3rd company to gain traction in the same market, with the same audience.
One of the only ways I could see Nintendo "return to prominence" as defined by many people, in combination with replacing Iwata as top operating officer, would be if Sony actually dropped out and another Nintendo exec had the right outlook and drive to move Nintendo into directly replacing the space they occupied. Hell, I could see Iwata voluntarily stepping down and eyeing a replacing he felt was good for the job, under those circumstances.
Otherwise, Nintendo's real problem is not something that I think can be easily just by swapping executives around.
I am a fan of Nintendo (among many things). I like Starfox and F-Zero too. But I feel fans have long had no perspective - just as Zelda, for example, has long been held up as a world beating event of gaming, when it's not really that big of a series in terms of popularity or sales. And the way fans can't comprehend why a game they turn their nose up at, like NSMB, sells 30 million copies.
What hardcore or enthusiast fans want, is not necessarily what the world wants, or what the world would even take notice of. There are plenty of people even right here on GAF, who are totally uninterested in Nintendo because of their games - as amazing as that might seem to many Nintendo fans. That's fine. Different tastes, different audiences.
But Nintendo just making Gamecube II and sticking a wishlist of fan favorite titles on it, isn't a magic bullet and may not really be as common sense as fans believe.