The biggest problem is that like games attract like games, and third parties follow the lead of the first party. The best illustration of this is probably that when Nintendo kicked off the Wii with a minigame collection as its killer app, everyone else followed with their own minigame collections and continued to do so right on through the rest of the Wii's life. Ditto with their lifestyle type software: Wii Fit, Wii Music, Brain Training, and so on. These efforts begat games like EA Active and Just Dance. There were efforts by third parties like Sega to "fill the void" for more typical (read: violent) games on the Wii, but these ended in failure mostly because that void never existed. The audience that Nintendo had established simply didn't want these types of games.
If Nintendo wants to compete for the non-Nintendo fan "core" (or whatever you prefer to call it), they will have to make games themselves that appeal to those gamers. A "Bayonetta 2 GET!" here and there would be nice but won't really cut it, it has to be a sustained effort.