cover doesn't need to cover whole screen, just the area the wipers cover and the wipers themselves.
I have found with some plastic covers they can leave an oily film on the screen when new which can smear screen, but probably no worse a smear than some cheap de-icing fluids cause.
The best de-icer I have found is Auto-Glym, a bit pricey but it doesn't take much, works fast and doesn't smear so probably works out cheaper in the end.
many places don't stock it (Halfords used to) but can get it on Amazon for £6 to £7 for 500mL pump spray bottle