Plastic headlight covers are the worse idea ever. Going in today to see if they can clean it up. It is so foggy you can hardy see the light. One of them was replaced 2 years ago when someone had the nerve to run into me.
Cadillac pioneered the trend, or so it would appear, when designers tucked away the gas cap under the left tail lamp assembly for the 1941 model year, then continued the practice for years until it became a Cadillac signature item.
Turtle Wax has a polishing/clarifying package for that, not too expensive but requires some time and effort. I used it and found it worthwhile.
I have been told that the degreasers resprayed in auto carwashes are one of the prime foggers of plastic headlights and other plastic trim.