True, but I think they were probably taken off dead Germans. You want your living prisoner shuffling around with his pants hanging off, or keeping pace?
If a German POW had a belt I wanted, he could spend the rest of the war with a piece of twine around his waist, or holding his pants up with his hands. I’d have taken them to keep them from being used to garrotte guards, or, Heaven forbid, the Hun bastid from hanging himself.