No, we agree about the phrase. But that's the whole ballgame: if "cradle" independently referred to the place, there would be no need to say "of civilization." It's an idiomatic use that is expressly non-literal. We also agree that "cradle" as a verb is not metaphorical.

Whether "cradle" is more or less common than "crib" (say) doesn't indicate one way or another whether its usage in other contexts is as a first- or second-order signifier.