Having re-read all of the replies, I agree that hip rocking might be a source of lower back pain. I'm still not convinced that it is less efficient than riding with still hips.

To those who separate efficiency from power, I would argue that power and efficiency actually go together. Power is what moves the bike. Efficiency is a measure of how well a given amount of power translates into forward speed. I think what you are actually referring to is the difference between aerobic and anaerobic power output in the body. Correct?

I guess I see it this way. Put a world-class sprinter on a trainer. Have him stand up and practice a sprint, using the same effort level as in an actual race. Since the bike is fixed vertically, one of two things will happen. Either he will rock his body back and forth, or he will keep his body more still, but he will put out less power than normal.