Formally, this is the bin-packing problem, which is NP-hard. There are lots of heuristic and approximate methods for coming up with configurations, but hitting an optimal configuration is unlikely to be done in short order.

I imagine load distribution, box fullness, rigidity etc can be included as dimensions to optimise. It'd be necessary, really, but doesn't make things any easier.

This is, however, what I believe Amazon are trying to achieve. As you point out, they have the advantage of knowing in advance what the different items being packaged are. They can presumably optimise within a single box, over a single order and across multiple orders and shipments. At their scale it would make sense to devote a large amount of compute to squeezing a few percent extra out of each cargo flight and truck delivery.