I’ve only ever seen the long, skinny “Persian” cucumbers in plastic and don’t buy them for that reason (maybe I should). Regular “fat” and pickle cucumbers are rarely in plastic, if ever.
Yes, not all cucumber are in plastic for various reasons. If plastic could be avoided, producers would avoid it as it don't bring any advantage from a marketing pov (aka it's not sexy like a cereal box is).
English cucumbers are usually wrapped in plastic because they have a thin skin and it helps keep in moisture, and it extends the shelf life.