I think for Dixie and Diddy Kong on the Wii, it's not that the Wii could not handle it; it's that the overall game would have less characters due to the amount of work that needs to be done for the pair. It's like how Pokemon Trainer was basically developing three characters. I think I remember Sakurai remarking that one possible character could have happened, but it would have taken the time of four other characters.
For Ice Climbers, others duos, and transformations, I think we are still far enough out where they can still fix these problems. Sakurai mentions that the team is experiencing problems; not that they are unsurmountable. For Dixie and Diddy or Lucina and Chrom pairings, I would prefer that if one of the characters dies, the other character disappears in a similar fashion to their game. For the DKC characters, they would start crying and then fade away, For Chrom and Lucina, I would prefer they fade as a unit does when it dies, along with the sound effect. If you zoom in on their face, you should be able to see them grit their death as they do in the large portraits before they die. This is of course if you can switch off between the characters. And you should only be able to switch the characters on the ground.