The main one I could think of was maximising 3D printer utilisation, I.e if filling your print volume was something you wanted to optimise for.

> Could give examples of use cases where dense 3d packing is needed? (Say, besides literal packing of physical objects in a box? )

Not an answer, but something interesting on this topic:

In a warehouse/distribution center, a dense packing result can be too time consuming for most consumer products. As density increases, it takes the human longer to find their own solution rapidly that works. You can provide instructions but that is even slower than the human just doing their best via trial and error.

We had to dial back our settings from about a 95% volume consumption percent (initial naive setting) down to about 80% before they could rapidly fill the cartons. Basically it's balancing cost of labor vs capacity of system during peak (conveyor would start backing up) vs shipping costs.

Bin packing can be seen as an optimization problem. In 2D, consider a scenario where you need to cut shapes from a sheet of plywood or sheet metal while minimizing waste; finding the optimal orientation of these shapes reduces material loss. In 3D, you might imagine packing objects into a container or cargo space, or sculpting a collection of 3D shapes out of a known volume of material, where you'd optimize the arrangement and orientation to minimize waste.