OK, here's my latest:

Canvas is there as a base for applying pastes etc to, which is something you can't do with your regular stropping surface.

In the barbers' manuals of olden times they say to prepare the canvas by rubbing in a white soap to fill in the voids. I myself rubbed in Dovo white to fill the voids. Before adding the white, the canvas was of little discernable value.

So, the canvas isn't helpful by heating the edge, nor by simple canvas friction, but rather as a foundation upon which to apply a fine medium.