The government has been involved in marriage because it has deemed the institution good for society. That's why there are tax breaks for married filing jointly, etc. The prevailing idea was that the government should promote marriage to establish greater social stability and make sure that children were provided for.
Those days are long gone. With the ease of divorce and the numbers of children born outside of a marriage, the government should no longer be involved in marriage. The problem is, How do you get out of it? Property laws, custody issues, etc. are all set-up. The government should get out of this altogether, but never will because everything is too intertwined.
I half agree with you… because I'm not sure 'marriage' should be a government concern either. You can protect people's rights without dictating the terms of something so personal as the marriage relationship. But I wouldn't say the 'days are long gone' where marriage creates greater social stability. Society is the sum of its people, and each person is born to a mum and a dad, and when those two are emotionally healthy, there is great benefit to growing up under their love and care. I would agree with those who say this is the ideal. Life is rarely ideal, but I still think there's value in calling a spade a spade.
So I'm defining 'marriage' here to mean a man and a woman who, in most cases, go on to create a family. And I'd argue (although I know I'll be unpopular here for doing so), that this relationship (recognised throughout every civilised culture throughout history as far as we know) is special, and as such deserves a unique word.
If it's discriminatory to have a word that only applies to a male–female union, then I suppose we should stop using any words that distinguish gender—wife, husband, woman, man, girl, boy, daughter, son, and so on. Some brands of feminism tried to do this, in the mistaken belief that it would create equality. Diluting our language and pretending there aren't differences isn't really addressing the source of bigotry. Why can't we recognise the differences (whether we're talking about gender, or sexuality, or race, or belief), but still teach and model love and respect?