dvcochran
Grandmaster
Agreed. In simple terms, If you step to punch and complete the step first, much of the body is no longer used in the power of the punch. Less mass is available therefore less power. The punch may use more segments of the body, but it would still be a segmented punch. As said, learning the step first is great for establishing a good base. If proper training is not continued, it is also great for learning bad habits. Conversely, punching way before the step is touching the ground hurts power. You only have the distance of the step to gain speed. I think of it as a car going 5 mph vs. a car going 25 mph. All that said, I think it is the acceleration we learn through proper technique that really makes the difference. And the confidence to use it.This was also one of the "secrets" that Jack Dempsey taught called the "falling step".
I also agree that the various methods of timing a punch are based on what you want to happen and are all good in that context.
In general, many beginners are taught foot first and establish a good base and then the punch follows. As you become better, you can apply many of those principles and hit with a whole body punch while in motion.