I've loved the same woman for close to a decade now, don't need a piece of paper to tell me how I feel, and neither does any kind of God, and if I did have a piece of paper and a 'blessing' from some guy that I paid a fortune to for it, it wouldn't change the future one whit.
It's not about the wedding or the piece of paper. It's about the legal benefits and rights that come with signing the contract.
Which is a large degree of what is wrong with it in my opinion, once upon a time people got married because they wanted to be married, nowadays, it's a financial concern, and that, in and of itself is merely a way to force people to conform, simple bribery.
Say the couple were married by a non-Christian denomination, or are part of a religion that doesn't have any kind of marriage ceremony? Do those benefits still apply (I'm asking in seriousness here, since I don't know the US laws regarding it), because if not, it's just yet another way of forcing a religion down someone's throat.