That's just the beginning. Assume that couple with children doesn't marry at all and the babymommy has two kids and a part-time job. She should probably pay babydaddy $400 or so a month rent to keep it legal, and claim not to know who the father is. She'll get subsidized health insurance or Medicaid, food stamps, a rent subsidy, a heating allowance and an Obamaphone. Because she's a struggling, working single mom just doing what she needs to do to get by, she'll stay under the radar for welfare dogooder interference. She'll get money back when she files federal taxes, and if he's under $30,000 or so his taxes will be minimal, probably even an insurance subsidy. If they were smart enough to avoid college loans, they're really well off...as long as they don't advertise with a big house or expensive car; just stay under the radar. It all falls apart if they get married or he identifies as the father.
I wouldn't do it; I'm of a different generation, more like an alternative reality. I do have to say though, the economics of this scenerio is compelling, and I can't imagine how anyone stops gaming the system once they buy in. It isn't even fraud.