Torie has already pointed out the weakness in your argument. Marriage is not only about procreation, and need not even have anything to do with it. I get frustrated when liberals say that marriage is about love and what business is it of the government if two people love each other. Marriage is not just about love.
Marriage is about procreation....more importantly it is about the shared responsibility taken upon themselves by male and female when they unite.
The reason for concern about these responsibilities is potential family coming from any union of male and female. That is the only (legitimate) reason why government has an interest in marriage. In fact, the reason the government prosecuted polygamist whasisname Green out in Utah was because that number of wives produced a whole courtyard full of kids....a burden on the welfare system...a consequence.
Therefore, they have an interest in polygamy. They could care less if all of Greens wives happen to love him.
Government is not concerned with who I love. They're concerned with the children born as the consequence of that love.