Sadly, it is still wise to have some third party involved to handle disputes over property (or, tragically, children) in cases of infidelity or abandnment. We still live in a fallen world, and not every relationship has a fairy-tale ending.

Marriage predates both church and state. Abraham's father had a wife. Free contract between individuals needs no higher authority. Though by all means, it is a ceremony most choose to involve all others in their life whom they value, which does typically include churches where applicable -- and often state as well, even if that value comes from a carrot/stick approach on the part of the state.