Well, one reason I've heard mentioned for colored belts was to give incentive to the kids to progress... don't know that I'd agree with that, it would not have appealed to me as a child, and at least one kids' class I've worked with did not have colored belts and did not seem to miss them, but kids are individuals, too, and many probably do enjoy the colors. Some may be more into the colored belts just for the visual effect, some for the rank thing.
Some who know me have questioned my attitude toward colored belts (don't like them) since I'm in the military, but I think the two are very different issues: rank is usually worn in the military to help maintain order and a chain of command, especially in light of a wartime situation that could disrupt and recombine units. But it situations I haven't experienced (POW camps, not in real life anyway) rank continued long after the uniform was no longer recognizible. In other situations, small units wearing civilian clothes, the rank and structure was still evident. So I think on the mat the leader is clearly defined, and after a couple of classes the beginner knows who to work with (or not work with, the other beginners)
Anyway, I was way past my youth when i started, but even as a child would have prefered the white-black only system.