I think it makes much more sense simply to eliminate government welfare payments for everyone, and it's just as possible as passing and enforcing a bunch of specific requirements for the case of legally-recognized polygamy.
Absolutely there should be no welfare payments at all. However, you will never eliminate welfare payments now. Too late! Experience shows once started a state cannot stop i.e.tThe Romans were still on the dole as Alaric was beating down the city gates. Welfare will only expand. I expect the government to provide “Free” tickets to various sporting events at anytime now.