Although.....can we just get rid of the law? Does the law have a function - for example, to guarantee the rights and freedoms of citizens under the law?
I say we can get rid of the law, because this particular set of laws on marriage function as an extension of religous principles--and we live in a society dedicated to the seperation of church and state (at least in theory).
Whether you're a Protestant thinking one spouse to every man/woman, or take the Morman view of "spread and multiply", the whole idea of marriage is mired in religion.
Speaking as a Christian, this is not a bad thing--I fully intend to get married into a monogomous relationship one day. But forcing these ideas of the "sanctity" of marriage or "family values" onto the general American public is like making the Bible required reading in school--it's forcing a particular worldview which under our Bill of Rights we have no obligation or compulsion to accept, legally anyway.
Marriage--monogomous, polygamist (one man, many wives), and polyandrist (one woman, many husbands)--has always been about economics--if a man was only sleeping with one woman (or at least a certifiable group of women, or a bunch of brothers sleeping with one woman), there could be no doubt as to the paternity of the child, and that child's place as the rightful heir of the father's land. The whole idea of marriage as a sacred ordained by God or what have you is fairly recent in western culture (though in Judeaic and Hindi culture, it stratches back a good deal farther).
The point is that we should really "divorce" marriage and the law--no tax breaks, no insurance benefits, no nothing. You should gain no more benefit from marriage than you do from going to Church every Sunday, which means some people are going to do it because they gain a deep, spiritual fulfillment from the act, whereas others won't see any reason to bother.
So, to sum up: The current view of marriage is a holdover of Puritan virtues, and thus marriage of any type (excepting the original post's exceptions--children and animals) should be neither encouraged, nor discouraged by our laws and government.
And that's my opinion,
YDD