It's not possible because of loading times.
Okay, I'll elaborate, but only because I'll look bad if I don't.
In Melee, when you played as Zelda/Sheik, both of them were already in the game's memory. The swap animation was mainly aesthetic, although there was a little bit of runtime changing some pointers.
In Brawl, the game stores only very small amounts of information about the other character while you're playing one of them. When you transform, it's actually loading the information from the disk into the game. It's not that much data comparitively, but loading from disk is much slower than loading from memory, and you must consider that the game is also progressing while the stuff is being loaded (as opposed to at the start of the game where the processor is focusing solely on setting everything up.
You can shorten transition times by pausing during it, lulz.