"Online" doesn't necessarily have to mean multiplayer in the sense of Mario Kart, Smash, Bayonetta or Monster Hunter. Super Mario 3D World has an asynchronous online play component in the form of ghost runs. Pullblox/Pushmo World allows you to create puzzles and share them with the community, as well as play puzzles that other players have created. Mario Maker, ditto. In NES Remix, you can post recordings of your fastest runs and challenge other players to beat them. On top of that, every first party title I own (along with some of the better third party efforts, like Deus Ex) integrates Miiverse in ways that create a feeling of being connected to the greater world (even if it's just something as simple as the message-in-a-bottle feature of WWHD). Saying that a console that does all this "doesn't do online" really doesn't sit right.
Personally, I actually find myself preferring this asynchronous approach as an alternative to the often noisy, hostile, grief-laden experience of interacting with randoms online. I would like Nintendo to keep rolling out traditional multiplayer experiences, but I'd rather see them concentrate these efforts where it makes sense: Mario Kart, Smash, Splatoon etc. (Hyrule Warriors would have made sense to me, but alas). Instead of treating multiplayer as a check box for each release, I'd rather see them invest those resources into developing and leveraging Miiverse - because it's actually kinda cool.
Anyway, I had no intention of engaging in a list war with you. I merely wanted to point out the futility of using guesstimates instead of concrete examples that would actually be useful to OP. This thread has concluded as far as I'm concerned, and I think OP made a smart choice given his situation and preferences. With that, I'm out.