As I and other people have said before, the two-characters-per-kart thing is more of a "logic" addition than anything else, as it just makes more sense to have one drive while the other attacks, instead of the attack magically plopping out of the kart. It would also make more sense if they let you attack in multiple directions, instead of just "shoot out front, drop behind." I'd imagine they do things a bit differently, say, using the shoulder buttons for acceleration (or just use one shoulder button for accelerate and the other for hopping, or use Z for braking, or something), and the C-stick controls attack-directions, sort of like vs. mode in SSB:M -- you move the C-stick to the upper-left, and the character attacks to the upper left. It would also mean you can kick and punch or something even if you don't have an item -- before, you were always limited to having an item or just ramming into them (which nearly always sucked, as you both got slowed down, and a CPU character was always able to get up to speed faster anyway). If you attack with the C-stick, there's SO many more options available that would be really easy to use. None of this "line up the shot just perfectly and fire and hope they don't move" crap that dominated the SNES and N64 versions. More like "fire at an enemy whenever and wherever they are! Trying to pass you? Try chucking a turtle shell right at 'em! Sneaking up behind you in battle mode? No longer are you defenseless until you haphazardly spin around!" And if they let you physically attack even when you don't have weapons, then it wouldn't matter about "triggering" the item first -- just hold the c-stick one direction and the character on back could keep attacking to the left or right.
Nintendo seems really keen on using both analog sticks as much as possible in their newer games, so I don't see why they wouldn't incorporate them both in MKDD. Can you think of any other use for the C-stick besides attacking?
Plus, it'd make the game so much easier from a party-game approach, or a "pick up and play" approach. Think about it. "This button makes you go, this stick turns, this stick attacks in the direction you press."