It is really hard to bring a putter face back to square when the stroke is a screen door motion. The two most important parts to an accurate stroke involve contact with the sweet spot, and face direction at impact. The screen door stroke , although it may work for some, has been proven not to be as dependable as an up and down the line, pendulum motion.
A lot of the square to open to square to closed motion in the screen door stroke offers a lot of oppertunity for movement in body parts that are not desirable like shoulders,wrists,hands, and arm roll.
I think a light feel in a putter leaves room for the little muscles to get involved. The more intense we become in our desire for accuracy, the more these muscles become active. This is fine on the practice green, but when the adrenalin flows, it goes right to the small muscles.