define biodegradable

What do you mean by "covers"? Do you mean packages and bags? They do make biodegradable plastics, but one of the main reason plastics are used for packaging in the first place is because of their durability. Much of their durability is due to the fact that they tend to be water resistant and inedible for most fungi and bacteria. Actually, plastics are more biodegradable than most people think. Especially thin plastics, like bags and other containers. Most plastic bags will breakdown if left exposed to the elements within a few years. Sure, they could last for centuries or maybe even millenia in a landfill, but then so can most materials.

More options for recycling might be the preferred option.

Plastics will breakdown, some a lot faster than others--try this--plactic milk or water jug, black roll plastic, or even a garbage bag---place out in sunny place hold it with a small weight to keep from blowing away come back in 3 to 6 months and they will crumble in your hands because of the Ultraviolet light from the sun. Other plastics have inhibators put into them when made example vinyl siding

Good idea, but if it was easy/plausible/effective, it probably would have been done already.