Investigating a cryptographic key found near a major military installation during war time doesn’t strike me as a waste of money. We have the full information about the outcome, but the San Diego FBI field office did not.
I think that’s what makes this story so funny- the FBI was acting appropriately and rationally, but ended up with a relatively absurd result.
If a Japanese spy knew this would happen, they could waste enormous amounts of time by spreading unused keys around San Diego.