The GameCube isn't built to be portable. Looking at the way the PSP eats up batteries, and how Sony even regulates how long developers spin the disc for, it doesn't make sense to build a portable GameCube, as many of the existing game are constantly spinning. They'd kill the battery in a couple of hours. Barring a very big leap in technology, it's not practical.
I'd like to see a portable GameCube, but I don't think it's technically reasonable. It might also confuse consumers, so it's not necessarily a wise choice marketing-wise, either.