I assume, that even in 1958, when "Ice Cold in Alex" was filmed, functional German half tracks were rare beasts, probably rarer than they are now, as nobody had much interest in fishing stuff out of rivers & swamps on the other side of the Iron Curtain - bear in mind that Lancaster ND759 which ditched on Lake Constance, Switzerland and it sank on 27th / 28th April 1944.,was recovered from the lake by Martin Shaffner during 1953/1954. It was put on display in Steckborn before being scrapped in 1955. A virtually intact Lancaster, with a known, wartime provenance, just scrapped.
Old British vehicles has probably rusted away by then & maybe the ex-US vehicles were just better, so had longer lives in civilian hands, when they were demobbed.