It's hard to tell exactly what's going on from the video. All I can say is when I have asked about this I've been personally told there must be no backwards motion by some people in the ITF with rank that can only be described as stratospheric. In the video it looks to me like Gen. Choi is holding his back straight and not letting him twist from side to side because that is the thing he is concentrating on teaching at that time. I've seen plenty of people teach and only focus on one or two things instead of everything that needs to be fixed. I do it myself at times. It's just a question of priorities.
I think you may have made a typo here as before I mentioned you negate the backwards motion by unbending the front knee. As a note, this shouldn't result in the front leg becoming completely straight. The front knee should remain flexed slightly. But as you straighten it the body lifts and then drops without the backwards motion seen in this video, which results in the settling down of the weight into the punch with no backwards motion taking power away from the technique.
Much like a sitting stance itself (a "horse stance") which has it's primary use as training the legs to get stronger, IMHO using sine wave while stationary is a training tool to get the students used to raising and dropping their weight. While a sitting stance does have other uses standing in one and throwing front punches is likely less directly applicable than the strengthening of the legs that is going on at the same time. Similarly, shuffling the weight in a stationary position does help you sink your mass into the technique, but it seems to be more important as a learning method so the student can easier generalize what's happening when actually stepping.
Pax,
Chris