The mud would instead form a solid layer on the windows, completely obstructing vision. I don't think wipers would survive close range mud bombardment either.

I saw a video somewhere where they have peel off helmet visors, so they just rip off the top layer to see again. Kind of like a post-it-note version of brand new screen protectors

Plexiglas (acrylic) isn't safe for vehicles.
You're thinking of Lexan (polycarbonate).

Those are brand names, btw.