First of all, most karate practitioners don't do that. From what I know, karate practitioners used to fight like that a while ago, rigid, etc. Then in the 60's things changed, I think some of it is attributed to Bill Wallace who showed the Americans that it's not necessary to hit from the chambered hand or using the back leg in order to gain power and that the footwork didn't have to be so set. The reason for this is most likely in misunderstanding of the forms. If in kata hands are rectracted to the hip, it's a finished move (say armbar), not a way to fight. But some schools still fight from zenkutsu dachi (long stance, spelling?) with one hand in low block and another one on the hip. Does that mean that all karate practitioners do that? No. Most people that I've seen have their hands up. So to sum up, they don't have hand down at the waist. It's a misconseption, I guess from the movies where the hands can be wherever they look better on the screen
Vadim
P.S. As for TKD, since in competition punching to the head is not allowed and hands are basically used to help balance the kicks, the hands tend to be all over the place. Would a TKD guy do that in a fight with different rules? I don't think so.