>A software cursor is manually drawn by the graphics stack, which saves what was under it, draws the cursor, and then whenever it needs to be moved, writes the original data back, saves the data at the new position, and then draws the cursor there.

AFAIK this hasn't been true for a long time on most platforms, certainly on macOS. The desktop image is composited on the GPU by assembling the underlying windows with appropriate effects like shadows and scrolling/scaling. A software cursor is just another overlay which may also have a transparent shadow.

Actually preserving what was under the cursor and putting it back is the sort of thing you wouldn't do anymore, because that's a cache which requires babysitting based on everything that's underneath and around it.

e.g. On macOS there's full screen zooming for accessibility, and if you wiggle the mouse, the cursor grows in size briefly (maybe even too big for hardware cursor to support).