That depends again on the polymer. All biological polymers are edible to some form of life. Some, like lignin (wood), are only edible to a few things (like mushrooms), but everything can be eaten by *something*. Starch, protein, and nucleic acids can be eaten and digested by humans. And, of course, anything organic can be combusted, if you get it hot enough.

A lot of artificial polymers have no biological process that can destroy them. They can be melted down and reformed into other objects, and as I've already said, sunlight can destroy them if they are exposed for long enough, as can extreme heat. However, the resulting waste of these reactions can be poisonous, and we do produce nylon and other things like it much faster than the sun can destroy them, so I would not rely on them as a recycling strategy.

The reason that reusing and recycling are encouraged as environmentally responsible is to reduce consumption of raw materials; the energy and materials used in production, packaging and shipment; and the wastes produced at each step.

With recycling, there's still shipping and re-maufacturing, but there's a lot less waste, energy use, and raw material use than for producing from scratch.

Re-use is pure savings, as long as it means re-use instead of purchasing new.

Today I saw some big signs for sale at a discount department store that said "Reduce, Reuse, Recycle." In other words, they cut down trees, shipped and milled them into boards, which they shipped out. They mined or recycled metals, and made hardware to attach to the boards. They manufactured paints, and applied them. They packaged and shipped the signs to stores. All so that people could consume an item reminding them to reduce consumption. Ironic, isn't it?