How much do you think it should cost a couple to form the contract for their marriage? Even a proper review of a contract with that complexity will likely cost a thousand or two, let alone making modifications. Times two, of course, as you would need independent representation.
I imagine that if we actually did this, fairly standard versions would start floating around and drop the costs - but the worst case of this is essentially the status quo with a few hundred in legal fees for review & education. Come to think of it, that wouldn't be terrible as it would reduce the amount of surprise in divorce.
On the other hand, it only really works in one jurisdiction so still problematic.
The government is not involved at the time of contract formation, there's not some government representative reviewing the contract. Nor do they enforce contracts (and related regulations) until there's a dispute.
Sure it does, depending on what the contract is about, even between individuals -- at least in most countries: A sale of real estate isn't really done until the deed is properly registered with the appropriate authorities. (I'm guessing this goes even for [at least most of] the otherwise so often wildly different USA.)
Marriage works the exact same way (again, at least in most of the world), and for the exact same reason(s): It only comes into force once properly registered, because it affects not only the parties and the relationship between them, but their relationship to government and the rest of society. For married people, taxation may change if the authorities know they're married; for property owners, they're the ones that can have others arrested for trespassing instead of themselves being arrested for it if the authorities know they're the owner.
That's pretty much how it has to work, otherwise it can't work at all. Isn't that rather obvious?