The only portions I disagree with is the part about adding more buttons to the Wiimote and the part about the instruction video. Adding the buttons would make the controller a bit more unweildly, unless you bulk up the Wiimote (and risk making it uncomfortable for some). It also risks the "too many damned buttons" syndrome that the Wiimote was meant to counter. As for the instruction video, I think the more elegant and efficient approach would be for the system to automatically search for nearby wireless connections upon start up, then ask you if you'd like to connect to a network. If you want to incentivize connectivity, maybe offer a free VC game of the purchaser's choice.
Thinking about it a bit more, I would also offer a second SKU, a sort of "family pack" version that ditches the Pro Controller and swaps in an extra Wiimote/Nunchuk or two plus a bundled game, so you can play multiplayer right out of the box. Man I miss those days...
Hm, yeah. Probably right about those buttons, because there wouldn't be all that many games that gain from them while it clutters up the controller. As for the instruction video, the point is really to make every owner of the system aware of it. I think there are many people who don't really know what they can gain by connecting to the eShop. Your solution paired with a pre-installed promotional video for eShop Virtual Console classics and new digital content wouldn't be bad. It's not like anyone would be forced to click on that video channel, but it would be an easy way to show off what people are potentially missing out on. One free VC game of choice is a great idea.
A second SKU is fine as long as it only differs in packed-in controllers and/or games. A difference that is easy to convey to consumers and nobody is going to feel that they bought a gimped product.