For those of you in the second group, the new "Boost Mode" in New Super Mario Bros. U is just the thing, replacing the pseudo-competitive bumbling with a simple, but enjoyable, and almost entirely helpful interaction.
While the game is going on as normal on the television, one player can tap the touchscreen to place blocks, which dissipate as players stand on them. Ideally, these blocks are used to help the Wiimote-based players reach secret areas, make difficult jumps, and avoid falling into Piranha Plants or other obstacles below. It's also possible to be a jerk and place blocks in the way of jumps, but I found that less fun than being helpful.
You can also tap the block again to make a smaller block that spits out a bunch of coins, and tap enemies to stun them. Sure, it makes Mario an easier experience, but it's also fun for everyone involved -- I enjoyed trying to land platforms right under a falling Mario with perfect timing, and I liked working together with another player to get through a level efficiently. And I certainly didn't mind having another player in my game who wasn't going to accidentally jump on my head.