I like the idea of connectivity but I don't think it was ever used in a very meaningful way on the GameCube. Four Swords, Pac-Man Vs, and Final Fantasy Crystal Chronicles are all games that could just as easily be online games. A game that better used the idea was The Wind Waker, at least, in terms of concept. There wasn't enough for the second player to do, so it wasn't very interesting. Still, connectivity is a good way to put a two-player option into a traditionally one-player game because it still allows the player to have the whole screen. All that it needs is a compelling aspect for the second player. There are a pretty limited number of ways it could be used effectively, but hey, it isn't like Nintendo ever uses their accessories for more than a couple of games.
I don't think connectivity is really meant as a replacement for online (and if Nintendo were actually pushing it as such back on the GameCube, it was a mistake). Games would have to be scaled back to run on the lower resolution of the (3)DS screen and different control inputs; Four Swords was basically a GBA game on a GameCube disc.