Civil Marriage vs Civil Union: Why NOT Leave Marriage to Churches?

I've heard many people on both sides of the same-sex marriage debate make the following remark: "Really, the state should stay out of the marriage business altogether. They should offer civil unions to anyone who wants legal standing for their partnerships, and leave marriage to the churches."

Well, why not? There may be reasons for the state to legally recognize and regulate domestic partnerships--but "marriage" is such a heavily weighted concept, fraught with religious and social significance. Why couldn't the state avoid all the controversy by just announcing that it's limiting its role to making legal contracts between domestic partners, without intending these partnerships to be "marriages," however that contested concept is understood?