Lizard Of Oz
Demented Avenger
You're saying that there is no other simple way to solve this problem than to have the government recognize marriage.
Because it makes no sense to be able to assign all those rights to your sister or your first cousin you are very close with or your daughter or your brother or your close friend that you have lived with for years because both of your spouses died and you have no interest in remarrying or any number of other legitimate scenarios that the current system is too broken to support right now.
Birth certificates or equivalent.
I would also like to point out that none of the issues you mentioned are foregone conclusions with this "one document". Otherwise, we wouldn't have divorce lawyers.
What about medical proxy? A spouse can make all medical decisions for the other spouse with nothing more than a marriage license. Can lawyers be brought into the equation? Certainly, they always can, but in this case they are usually not. The point being that the spouse need not produce reams of legal documents to prove anything. As simple non-government church wedding can not do this, the couple would be required to hire lawyers and negotiate a marriage contract. And then, in an emergent medical situation, one spouse would have to produce that contract to prove medical proxy, then the hospitals lawyers would have to review the contract to make sure everything was on the "up-and-up", before they could do anything. Not only does this apply to medical proxy, but also to just about all the things I listed above.
Marriage is a legal matter just as much as it is an emotional one. What we need to do is get those bigoted churches removed from the process.