I was just looking at a list of old Nintendo games, pondering which ones could be improved by the remote, when I found Mario and Wario. I had forgotten all about this game. It's essentially a puzzle game in the same vein as Lemmings, only instead of a horde of mindless critters, you guide a blinded Mario. It was played using the SNES mouse, with which you controlled a fairy who interacted with elements in the environment.
Now imagine that instead of a point and click interface, you actually used the remote to affect things more directly. For example, you might have to turn a crank to raise a bridge, or use a rope and pulley to lift something, or cut a rope to drop something, or fan a fire to burn something, or get Mario to hit a switch at the same time you do. What you could do would depend on what tools were available to you in a given level.
Who'd develop it? Well, Game Freak did the original, so they might as well do this one. They've shown that they still have what it takes to develop non-pokemon games with Drill Dozer.
2d or 3d? I'm not sure. guiding Mario through a 3d environment without being able to control him directly could be cumbersome, but puzzles using the remote would probably be better in 3d. I'll say 3d, with set paths for Mario to follow so you don't have to worry about getting him lined up just right to not walk off the side of a bridge.
The only problem is that I don't really expect an announcement at E3, or a return of this game ever, for that matter, but you got me thinking.