I doubt the Wii would have been released without the Wii-mote. It seems fairly clear that the Wii-mote could have been introduced as a Gamecube peripheral, but would not have achieved much market penetration on that basis. The choice Nintendo made was to make the Wii-mote the driving feature and market the system as a new generation, taking advantage of some technological progress in the meanwhile to make the system consume less power and be a bit of a step up from the GCN architecture.
So far, this appears to have been the right choice -- consumers at large are proving to be much more interested in having something new, fun, and yes, even short-term to do (the Wii-mote) than digging deep into fancier iterations of existing gaming styles. And the Wii is inexpensive enough that hardcore gamers can afford a Wii as well as an HD-capable system.
(On that note, I think Nintendo is indirectly benefiting from the equivalent of a format war on the HD end in some markets -- the more multi-platform releases come out for both PS3 and 360, the less differentiation there is between them. It's easier for consumers to buy the cheap/now system and take a wait-and-see attitude on the high end. I know I was happy to buy a Wii but haven't quite made up my mind between the two high-end systems yet; to some degree the decision comes down to esoteric concerns about A/V and internet hookups for me personally. And if the Wii software flow picks up, I might not be in a rush until prices drop and the libraries grow for both HD consoles. I suspect this kind of fence-sitter's delay is playing into the market right now.)
