The problem with re-using a box is that it loses a lot of integrity after the initial shipment. Its crush rating is reduced and chance of tear increases sharply. Many damaged and ripped parcels at the post office are due to box reuse or bad packaging combined with incorrect crush rating.
It would have to be inspected to make sure its ok to re-use. Does not have to be cardboard.
Agree, that would likely work or a solution could be found.
Perhaps it could instead be sent back to Amazon for recycling?
Peapod has demonstrated that no, you wouldn't actually want this.