I, personally, could care less whether you’re married or not. The state, however, has an interest in determining if you’re married because the state so often plays a vital role in your “unmarriage.”
This is the principle difference between marriage and baptisms or bar mitzvahs or confirmations. You can’t become unconfirmed. You can’t annul your baptism. You don’t give back bar mitzvah presents if you convert to Christianity at 14. You can get divorced. Now how do you separate out who gets what?
If everyone could settle everything amicably, you probably wouldn’t need a marriage to be legally binding. But heck, if we’re gonna go there, you might as well say “If everyone could settle everything amicably, we wouldn’t need 90% of the government.” Technically it’s true, but realistically shit is going to hit the fan from time to time and people must be there to sift through the pieces of corn.