There are two that I think really makes sense:
* Animals can haul to the non deep part of a storage. That is, the top 2 stacks for a size 2 storage unit. This makes deep storage a improvement rather than a trouble for certain cases. This at least makes sense for shelf. Deep shelf should still allow easy access of the normal space.
* Bond animals can haul to the storage. Bond animals are affected by their master and become smarter to use deep storage.