I wanted to add something to this. Correct me if I'm wrong.
I never understood how you could get any weight transfer to your back leg on the backswing by having a centered hip turn. In baseball, most power hitters load up on their back leg and have lateral motion of up to a foot. For a pitcher it's the same thing. A windup allows you to load up on your back leg by swaying back considerably, and then you explode outward with the energy stored on your back side.
I was told in my first evolvr lesson to try this drill to reduce my lateral hip sway on the backswing: Put a basketball between a wall and my left hip, and then practice taking backswings without allowing the ball to drop. This would ensure that I wasn't swaying backward, but instead rotating, else the ball would fall as I moved. I noticed that even though I wasn;t swaying, I still felt a powerful tension in my rear leg - the same kind of power that I achieved swaying back. Here's my take on why this is true:
At setup, your hips are parallel to the target line. When you rotate, though, your body's center of gravity is moving backward because the bulk of your upper body is now behind the center of your body. The mere fact that your body's weight has shifted back, even if your hips have not swayed laterally, ensures that your weight will plant on your rear leg more than your front. By not moving your hips backward, though, it makes it much easier to produce a tremendous amount of weight transfer forward on the downswing because you don't need to "recover" from the lateral movement you used to load up on your rear leg. It's a more efficient means for generating power.
Is this analysis correct?