I want to see the no-nonsense, games-first approach of the GameCube, with the functionality of both living room-based console and handheld device. I give you: the GameFrustum.
Ok, so the name is up for debate (though it's still better than the Wii), but the functions entail everything I would want from a Nintendo machine. It's a box with all the faffery of second screen controllers and plastic wand-waving sliced away. In the absence of these peripherals Nintendo would be forced to look long and hard to innovate at a fundamental level, ensuring that online services are up to snuff, that voice chat and social systems work across multiple devices, and that its third-party offerings in-between its own sizeable gaming events are enough to ensure its machine isn't the first thing I unplug when considering which HDMI to free up.
Let's fling just a bit of hardware wizardry in there. The top section of the machine can be completely pulled out, and is basically a 3DS, capable of playing the hefty back catalog of Wii, GameCube and N64 games that would crop up on the new eShop. Oh, and as we're due to get Nintendo games and services on phones now, how about having each slanted side of the device also act as a charger? Just rest your phone/tablet/pad against the machine to charge when not playing.