I'm going to agree with you that moving fewer parts makes you more accurate, but I'm going to disagree with you about whether having more momentum behind the cue generates more power in the shot, and thus "more action". If you stroke with draw, for instance, at 50% speed, and then shoot the same shot, same arm speed, while shifting your weight back then forward, there is a noticeable increase in the amount of backspin you impart on the cue ball without doing any more work with your arm. If increasing your arm speed up to the 90-100% range makes you lose your accuracy, then you may find that shooting at 50% with a body weight shift actually gets you the same end result with.. more accuracy. I'm not saying it's a good idea, I'm just saying it's a palatable workaround for someone who lacks the arm strength for a particular shot. That's probably why so many peope shift their body weight on the break. They want more power on a shot that still needs to be accurate.
Shifting my body weight is the way I used to power draw. Now I've learned to do it with just my stroke, but only because I've improved the accuracy and speed of my stroke once I found out what the hit was supposed to feel like. There are lots of things I'll try at the practice table that will lead to things that are useful during a match.
But thanks for telling me I'm wrong without actually disproving what I said.