The fact is, weapons were brought home, in both approved ways and un approved.
My father was a WWII vet of Europe.
He told me that an uncle brought home an M1 Thompson SMG...the uncle served on a navy ocean going tug which pulled landing craft off invasion beaches. My uncle was in the beach party under fire, and armed only with a 1911. He picked up the Thompson, and kept it for the rest of the war. When my uncles ship docked in San Diego, he walked off with his sea bag and the Thompson over his shoulder, and nobody stopped him.
According to my dad, they fired it one time at an Ohio farm in the late 1940's. My dad said it scared great grandfather so much, that the old man took the gun and buried it somewhere. They are all dead now, and no doubt, that Thompson is a pile of rust.
My father was a weapons expert in his Cav unit. He had a collection of German automatic weapons on his armored car...MG42, MG34, and others. He used them to familiarize other units in the German weapons. He had arranged to have them dewated in France to bring home, when he got dysentery and went in the hospital. When he got out, his unit had shipped out for the Pacific, and all his stuff was gone. As an aside, the atom bombing in Japan meant that his unit beat him home...their ship just changed course mid trip.
My father brought home two pistols from his service, both properly papered. I have one, and my brother has the other, and we both have the paperwork.
Mine is my most reassured possession...it is sad that future generations won't get to have such heirlooms of the service of their relatives.