It isn't necessarily apocalyptic, but we do a lot of things to address wood biodegrading. Paint, arsenic-impregnated wood, etc. If we didn't have any such measures, our use of wood would quickly be a problem.

Also, a lot of current uses of plastic have a built-in assumption that they don't degrade. We could adapt, sure, but it would be quite disruptive, and a lot of current uses would need to be changed/replaced.