Women being given a financial reward by the State for raising babies by themselves has nothing to do with a society that establishes marriage as between a man and a woman so that children will have a mother and a father.
You have your eyes shut pretty tight on reality. For the last 50 years, marriage licenses have only been between a man and a woman. Out of wedlock births have gone to over 50% from single digits. For those who do bother getting married, divorce rates are also over 50%. And you say the welfare state that brought that on isn't the problem, and that getting the state completely out of the marriage business will somehow "really" encourage anti-family behavior??? No the problems monetarily based, not esoteric.
Any two adults are currently allowed to live together and tell anyone they wish that they are married, without the threat of a criminal charge, ergo its legal. Well, I would throw more facts at you, but you appear to be immune.