I don't think "natural" is used metaphorically. If you had an accurate simulation of the human hand you could show that one of the directions minimizes energy usage and damage to your hand, and I think it's the one we use. Starting high means gravity is helping you move down the page, and it's also easier to move your hand towards you than away from you, and the many small movements (rather than the one big one to the top of the next page) are where more energy is spent because of friction.

Writing is done by people and people are almost always subject to gravity. It's one of the 4 fundamental forces. Energy minimization is not an arbitrary selection criteria, it's central to the fitness/design of all living things.

I can agree moving down the page is probably more common due to human mechanics, AND say that trying to make the argument the way they did wasn’t particularly sensible.