Government involvement in licensing marriage, and related matters such as inheritance and rights to make medical decisions, is the problem. In my view, the best way to deal with this is to return marriage and related matters entirely to the private sector. I do not understand what you mean about "the private sector.' Laws regarding property are explicitly a government function. Property ownership and its orderly transfer are a large measure of the foundation of a successful society.
Otherwise, if the gays win on the same-sex marraige issue, there would be no legal foundation on which to bar polygamy, adult-child relationships, and the like.
This is one of the reasons that the Supreme Court decision about the prime 'right' being the 'right of privacy' is a wrong decision.
"Private sector" means exactly what it says. The government does not have to license marriages in order for — as you put it — property ownership and its orderly transfer to occur. As many others on this thread have already pointed out, the purpose of marriage was and is to protect children, mostly, but also women. Until the very recent availability of DNA analysis, marriage and at least the prospect of monogomy was the only way a man could have some guarantee that he was, in fact, the father of the children to whom his wife gave birth. Inheritance laws and customs developed on that basis.
I don't know when government got into the business of licensing marriages, but I'd wager it was in relatively recent times — perhaps the mid-to-late part of the 19th century. Before then, most marriages in most societies were based in religious and cultural traditions, i.e., the private sector.