Keeping weight on the back leg and having the body slightly tilted away from the pitcher will allow for full rotation. Throwing weight onto a stiff front leg and bringing the body to a more vertical position will have the effect of limiting hip rotation. You can check this out for yourself. Stride with the front toe closed. Now, cast your weight onto a stiff front leg and note how restricted your hips are.
Many batters let go of the top hand in varying degrees.
Swinging at an outside pitch can also result in less shoulder and hip rotation and therefor the need to let go of the top hand.