Just set a screen saver that says "Don't touch me"
Besides, who actually uses screen savers these days? Don't most people turn off their monitors or put them in energy saving mode at the end of the day?
They typically empty out wastebins and attend to the bathrooms.
Makes it easier to clean and protects the paint
I can tell you that if I bought one of these monitors, I wouldn't have read the manual, and I would have thought of the free cloth as one of those "nice little touches" that always comes with buying an Apple product.
If I was buying the monitor after seeing the headline, I would probably try to find a safe dust cover to put over the monitor when not in use to help prevent avoidable mishaps from someone being a little too enthusiastic about cleaning my work area.