I picked up this Stevens Walden socket set the other day, and on the contents, it lists a 5/16 hex key. The hex key is missing, but what was it for? There is nothing in the set that needs one, that I can see.
You and your question are in good company, Mick. GJ member and Walden collector four.cycle has brought this oddball mystery up before. It's a true headscratcher.
I don't remember the size but the differential fill plug on my truck has an Allen head. I could see different stuff using that enough to just throw it in there, it couldn't have cost them too much.