I think some of the problem has been the fixation (pun intended) on the word "fixed".
Should that be "fixed in relation to the position of the sun", "fixed in relation to the winch" or "fixed in relation to something else entirely"?
Almost all of the diagrams and videos illustrating a single pulley don't have the end of the cable attached to the same object as the winch. So it is understandable that most people get the impression that there is no advantage when the pulley is attached to the tree.
It becomes quite a different situation when the cable is attached to the same object as the winch.

