My Big Problem with Big Love

Actually, it's a problem with the law surrounding polygamy. How is it illegal? I mean, take the show, for instance: Bill is only married to one woman, Barb. He has a legal marriage with her and "legitimate" children with her. He has this unrecognized relationship with the others. Where's the problem? He's not stealing from the people by getting unwarranted public aid benefits. He takes care of his family and they entered into it willingly. Where's the beef?