Many Golden Age comics I've seen have covers which did NOT depict a specific interior story in that issue. Some did, but I'd say many (perhaps a majority) did not. There are good logistical reasons for this, and it probably varied by publisher.
Harvey had a clever little twist, as seen on this issue (but used quite a bit): include a text feature on "The Story Behind the Cover." The topically-relevant ("foreign agents," presumably communists) cover says "Be sure to read 'The Enemy Attacks'" and technically it's correct -- a one-page text story, in this case.
Link to the book:
Joe Palooka Comics 059