I don't think there was any rhyme/reason for it other than simply preference by any given person at any given time. I definitely don't believe it was an issue of brass usage or availability, jmho, the minute difference doesn't really seem enough to matter.
My personal opinion is that those using the full wrap felt that it was stronger or better protection against forestock splitting, especially given the proximity to the forward barrel lug which creates a weak point in the forestock a predicate to a potential split as it's centered. But, they just couldn't figure out how to attach an end piece to cover the exposed wood (or maybe just didn't care!).