[Lurking Libertarian]

It dawned on me that some states recognizes “common law” marriage where a man and woman who have lived together for a certain length of time are considered legally married without going through with the actual ceremony, perhaps even against their expressed desire.

I am not a family-law expert, but, based on what I remember from law school, common-law marriage requires that the parties not only live together, but that they tell other people that they are married. So it can never happen "against their expressed desire."

[Albion Wilde]

I agree from my memories of ConLaw class in grad school; they have to “hold themselves out” as married in order to have a common-law marriage recognized.