since you apparently didn’t understand what “intestacy” means. I do understand it. It's a fancy legal term for "morons who didn't plan ahead."
They don’t have a will.
Then they're idiots and the State will take the property in accordance with the Probate laws of said State.
Nothing in this scenario you posit requires the State to have anything to do with the institution of Marriage.
L
Okay. Fine. As long as you're aware that intestacy is just one minor issue arising from the abolition of marriage as a legal institution. Most people who advocate "getting the State out of marriage" don't think about such repercussions - the idea of the State acquiring the property of the dead when there is a spouse still living is anathema to them, and it gives them pause when I point out that very simple example. Since you appear to be aware of all those repercussions, I don't need to point them out to you.
That said, I still don't agree with the elimination of marriage as a legal relationship, for a variety of reasons. However, I see no need to discuss those reasons here.