As a challenge: try to separate waxed cardboard food containers from polyethylene-coated cardboard food containers. They look almost identical. They feel quite similar. Nonetheless, the former is compostable, whereas the latter is not and also contains non-recyclable plastic. (Good luck getting the polyethylene off the cardboard. Maybe you could derive new polymer feedstock from the whole mess, but this seems no easier than turning compostable waste into plastic in general.)