That's a clever point. Maybe there are two uses for an analogy, then: (1) to reason informally (performing a logical argument using natural, more familiar, language). This could (and I think, should) be done formally whenever possible. and (2) the use as an "intuition pump" (word from Dennett, I think) where the point is to provide a tangible analogy to your model, enabling someone to "understand" you, but not necessarily proving anything.