...When production personnel and actors refer to the Enterprise as another character in the show, they are speaking metaphorically, not literally, to elicit an emotional response and sense of connection. It's employed as part of a different rhetorical strategy than adherence to strict literalism and precise diction. As part of a public relations strategy, the use of language with more emotional connotations serves a rhetorical purpose that a simple, factual, 'The Enterprise is the setting of our stories, our vehicle for getting our characters where we need them to be" does not...
There are contexts in which "The Enterprise is a beautiful lady and we love her" is preferable to "The Enterprise is a wooden filming model constructed by Richard C. Datin," and other circumstances in which the converse is preferable.