My first thought was to make the box itself of some kind of mesh which ordinarily behaved like netting, but could, if manipulated in the right way, become flat and inflexible. I suppose that’s possible, but from my almost wholly ignorant standpoint it sounds like science fiction. A second idea was to have a box with a removable, inflexible top section and a bottom section that could fold down and be stored ‘inside’ the top section (in fact the lid of the top would have a lip that would keep the bottom in place). The problematic padding question would be solved by using a lining which, when inflated, follows the contours of the objects it comes into contact with. (Another science fiction idea? Surely there are many materials that can do this.) I wondered whether this might take the form of a sort of quilting of small pockets which when inflated provide a buffer for the object the pockets being small enough for the ‘quilt’ to mould itself round the object and then behind this was a second ‘quilt’ using larger pockets which when inflated would fill out the rest of the box. (Perhaps there would need to be a third or even fourth layer of even larger pockets but how bulky would these pockets, even when empty, turn out to be?) It seems probable that in some cases the object would need to be fixed away from all the edges perhaps using some form of adjustable scaffold/cradle to raise it from the bottom of the box. The idea would be that the pump used to inflate the lining would take the form of something like a key in a piece of clockwork: you turn it to inflate. (Presumably the pump used could take advantage of any new advances in pump technology given that there is a certain environmental impetus to this idea, it would be better if it was hand-operated.) This inflation would also affect the flexible walls of the bottom section, pushing them out so that at the top they are wedged in place around the lip of the top section. The ‘key’ used to inflate the box lining and ‘lock’ the box would also be used to deflate and unlock it at the other end. The idea is basically that the recipient of the box would have a key of their own (which assumes, of course, that this system would become more or less universal) so that the sender would not need to send that as well, but it occurs to me that this key could with relatively little difficulty become like a real key: if the shape of both the key and the ‘keyhole’ in the side of the box could somehow be adjusted, then the box would be that much more difficult for an intermediary to open. The ‘code’ used to adjust the key so that it fits the hole could be sent to the recipient separately. NB I had conceived the top and bottom of the box to be separate, but it might make more sense if they were connected by hinges along one side, ie the back. It would be good if the key could have a second function to lock the flattened bottom section to the top for storage (perhaps some kind of quoin effect on the base of the bottom section), and better still if the method used to do the locking kept the key attached to the box: that way, all three parts of the box would stay together and not get lost. The ideal materials for this if they are up to the job would be recycled plastics: this is after all yet another packaging problem… Hopefully plastic would also make it easier to remove any mailing labels, stamps, etc placed on the boxes, so that they can be used again. (Or maybe the locking method that is doing all those useful things mentioned above could also be made to keep an ordinary piece of paper (in a standard size, say A4) in place on top of the box: this would then be the only part of the box that gets thrown away, with the address and stamp stuff on it.) Because of the use of an expandable lining, you might be able to get away with a relatively small number of box sizes.
Alternatively… perhaps one could suspend the object in the box from the eight corners: the object would sit in a sort of netting bag attached hammock-like to the corners with strong but flexible supports. When the box was packed, the user would pull on a draw-string and the object would be secured: able to move slightly but not very far. (This sounds like the sort of thing you might have found on an old sailing ship, complete with creak.) Given that some of the objects are likely to be fairly large and heavy, it might be worth combining the two approaches: the object could be placed on a relatively shallow bed with plenty of give (in other words, using some form of air-, ball- or liquid-pocket technology) and could then be fixed there with netting and corner supports. The bed would be a permanent fixture of the box, but would hopefully not be deep enough to prevent the box from being folded away conveniently. One advantage this one loses over the ‘inflation’ idea is that the (slightly) compressed air in that version was what gave the sides of the box their rigidity: once the air was removed from the air-pockets and the pressure was normal, the sides became flexible again and could be folded away. Would it be possible in this ‘hammock’ version to combine the ‘draw-string’ effect of covering the object with netting and keeping it in place with supports from the corner, with making the sides of the box rigid? Could the edges of the box be hollow, so that ‘at rest’ a series of stiff rods were in the bottom edges, and then could be drawn up into the side edges (via a curved connection between bottom and side edge) and when the draw-string was pulled tight, the rods stayed in the side edges and gave it rigidity?