does this mean there is no state interest in divorce either?
Which is exactly why the state should have no interest in "marriage" in the first place.
You have an entire sector of the legal profession -- divorce attorneys -- who are dedicated to all of those cases where a so-called "contract" is broken by one of the two people who signed it. This in and of itself is irrefutable evidence that the state has no business getting involved in marriage. If real estate contracts were broken with this kind of regularity, you could never buy or sell property in your state. You can't even imagine a bizarre situation where you buy a home from someone, only to have that person come back ten years later and sue you because he didn't like the deal.
Divorce can be handled as a matter of contract law.