I can't seem to find anything definitive that identifies the legal grounds to claim that the storage of cash in a safety deposit box is illegal in the United States, but I did come across a couple of references that indicated that certain banks have included the prohibition in their terms of use.
Given that the contents of a safe deposit boxes are not covered by FDIC insurance, I can see why it's not necessarily recommended.
Given that the contents of a safe deposit boxes are not covered by FDIC insurance, I can see why it's not necessarily recommended.