Sony and MS will go nowhere near Nintendo's 'strategy' next generation, if anything, Nintendo will be forced to go further in the other direction.
Addressing what Nick said, it's not about 'waggle', just like it's not about 'selling to women'.
It's about time. And the time problem is two-fold, it's learning curve and time spent in game.
Nintendo created a system that has virtually no learning curve and allows you to pick up and play the majority of the games for a short period of time. You don't need to spend hours learning how to play, or hours at a time playing the system. The interface was ideal for this, not only for ease of use, but also because the lack of precision made it almost impossible to become 'expert' and make games uncompetitive against 'casuals'.
It mirrors the 'keyboard/mouse' FPS argument almost to a tee. Hardcore gamers want to be rewarded for their thousands of hours of investment in a game. They don't like the fact that gamepads remove that reward and even the playing field. The Wiimote did the same thing, but to an even bigger degree. I used to be one of those 'KB&M' FPS snobs. As I've gotten older, I don't have thousands of hours to invest. Most PC FPS, I can't even play (multiplayer) without getting schooled so rapidly it's no longer fun to play. I can work the 360 controls well enough with a small enough learning curve that I can hold my own most games. Sure, those who still want to put thousands of hours in can beat me senseless, but for the most part, the controller dictates a certain baseline of playability.
So it's not 'waggle' necessarily, it's about flattening the learning curve. Flattening the learning curve, allowing gaming experiences to last 30 minutes instead of 3 hours, and an affordable cost of entry were the keys to the Wii's success.
I think the rest of the proposed reasons (demographics, pop-culture relevance, etc..) are ancillary.