When people talk about "getting government out of marriage", they are talking about marriage between consenting adults. I think you are throwing out a red herring. I don't see any of the "get government out of the bedroom" crowd arguing for government to not intervene in cases of rape and other forms of sexual abuse.
No, what they're talking about is a slogan that has no actual meaning. Often it comes from angry bigots who can't stand to have to share marriage with people they think are icky, and are more willing to destroy the whole thing than think about two men having sex. It was then taken up by anti-government types who just complain that the government exists. There is never an actual list of laws that anyone wants changed, merely railing against the issuing of marriage licenses. The many many many laws that deal with marital status are just assumed to all be resolvable by private contract, which is absolutely not true. One such example is that spouses are not required to testify against one another. Without a legal status of marriage, how would that work? There are often complaints about tax benefits, which is strange for the anti-government types in that they are arguing for people to pay higher taxes.
And the distinction between being issued a licence to marry, and having a marriage contract that either can or cannot be enforced in a court is mainly a semantic one. At some point, someone is going to say that they are or are not married, someone else is going to disagree, and the government (probably a court) is going to have to decide one way or the other. It is a meaningless demand based primarily on semantics.
And let's talk about the consequences of making it harder to prove one way or the other about a marriage. Consider also a lack of marital status on inheritance. Sure, it's easy to say that everyone should keep an updated will, but what if they don't? Suppose I die tomorrow, and three people show up to claim my stuff, all claiming to be my spouse. They all say that we had private, oral contracts (which are frequently enforceable in court). I'm dead, so you certainly can't ask me which one, if any, is really married to me. Or suppose I'm not dead. Suppose I'm injured, and in critical condition. My spouse shows up at the hospital, but I was not able to designate anyone to be my medical proxy. Who now can decide if I should receive the experimental surgery that could save my life, or rely on the less effective but thoroughly tested methods? There are far reaching implications of abolishing marital status as a legal status
The "get government out of marriage" types have only two agendas. There's the ones who don't want gays to have the same rights they do, and the ones who just blanketly oppose government. Oh, and there's the state's rights crowd who are a weird combination of the two. It's an argument that is rooted in ignorance and bigotry.
