I don't see how the analogy requires or implies the creation of economic value or productive work or any other particular use of the money, only that the money put in today is being used today for whatever purpose.

Again, I'm not arguing for or against Social Security, just whether or not the original analogy is apt. If it's not, it does no harm to those arguing against Social Security unless the argument relies largely on the analogy being sound. I can't imagine that's the case at all. If it is apt, I think it likely can be expressed in a way that more clearly shows its intent.