I’m sorry, I’ll make this clear, since you apparently didn’t understand what “intestacy” means. They don’t have a will. Assume they also don’t have living blood relatives. They have a spouse. Since the law under this scheme will not recognize marriage, who gets their estate? The State?
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