My Dad and step-Mom did this; church only, no State.
Discussion
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.
In cases of infidelity or abandonment, the man can be dragged into court for his wrong-doing.