Nintendo has tried to connect its consoles to its handhelds in the past, with some success. The feature never really took off, but at least it was there. The Wii U's controller acts in a similar fashion, projecting a seperate view into the game directly to the controller. If the Wii U can do this with the controller, then it should be able to do so with the 3DS.
Nintendo says it's technically possible, but there "are some limitations" and they're afraid consumers are going to ask "Why does Nintendo force us to buy both systems"?
If the 3DS were connected to the Wii U, the "Wii U will not be able to access the Internet" unless Nintendo adds "special hardware".
Special hardware isn't really an option, either. Nintendo doesn't want to be perceived as "a company that made the Nintendo 3DS a controller because it wanted consumers to buy both hardware systems".
All of this is utterly ridiculous to me. Nintendo should stop gimping its hardware so it's capable of doing more than one thing at once. Also, quit being so paranoid - consumers aren't going to feel like Nintendo is forcing them to buy two systems, so long as it's optional. That stance is a little odd for Nintendo, who weren't afraid of making consumers feel like they had to buy accessory after accessory with the Wii, which has the Wii Fit, Classic controller, wheels, gun attachments, and so many more.