3rd party games will sell if they are comparable to the PS/Xbox versions. Contrary to popular belief people do actually have reasons other than 'eww Nintendo' for not buying Nintendo consoles and all the 3rd party games on them that they would buy anyways. Take away those reasons by being similar enough to the other consoles and Nintendo open themselves up to the huge multi plat audience of gamers.

The Gamecube example doesn't really work at all. Remember the original Xbox released that gen as well, that too had third party games, was powerful and wasn't overly expensive. It didn't really matter what they did that gen though, PS2 was just set up to win regardless of the competition. But look at what happened to the Xbox after that, MS went for a more powerful console, got all the 3rd party support and massively increased their sales. Nintendo boosted their sales a different way, but that way was clearly a one off, while the way Sony and MS have been doing it has worked many times and still does.

As I mentioned before they could have a solid hardcore console and then try the new stuff on top of that. The Xbox 360 released a year before the Wii and was only $50 more expensive. I expect they easily could have boosted the Wii's specs while still retaining some profitability, even if they only broke even on console sales the software would make up for that. Just imagine if they had the same specs as the 360, were just as easy to develop for and had an optional standard controller at launch. They would have got all the 3rd party support, had Nintendo's 1st party, motion controls and would still have been affordable. With both the casual audience they got and a chunk of the PS360 audience they could have matched or even exceeded PS2 numbers.