Many, Many, Many Americans get married without involving a church at all.
Even those that do involve a church, make sure they conform to the secular requirements. An American marriage license doesn't have a spot for which church married them, nor does it have a spot for the churches approval/disapproval.
If you were to look at the documents of a married couple you would be hard pressed to know their religion, but would know the government entity that approved it down to the county level.
[snark on] and 50% of them dissolve with the assistance of lawyers.[/snark]
How is that not more like a contract?
That looks like a false dichotomy of either govt or church, and if it's not a religious ceremony, it's all government's territory. I think you're leaving out the very large part that personal, familial, and social motives play in marriage vows. For example, as a religious person, part of my reluctance to divorcing my wife would be the fact that I gave my word to God that I would "have and hold for better or worse," etc. But I've never heard of anybody saying, "Hey, Jim, how can you do this? You swore to the justice of the peace that you would love her always in sickness and in health, and now you're just blowing it all off?". If we're offended about someone leaving their spouse, it's usually because the spouse is terminally ill, or because we think they should stay together for the children, that sort of thing.* The government is just a functionary that keeps the records, and demands some i's be dotted before the arrangement is done away with.
*My point is not that people should stay together for their children. I'm not looking to start that stupid debate.