Utah defends constitutionality of anti-polygamy laws

In a lawsuit currently pending in Utah, the family featured in Sister Wives is challenging the constitutionality of laws against adult, consensual polygamy. I've argued before that adult, consensual polygamy should be legal, but it's pretty hard to draw that out of the Lawrence decision. In any case, the state filed its memorandum yesterday. Although they're probably right on the law, I'm surprised at how badly written it is. (Hint to law students: never use the phrase "don't go there" in a pleading.) One question remains: if the state can forbid polygamy because of the social ills that sometimes result from it, or the abuses that at times occur, can the state also ban marriage in toto on the theory that doing so will prevent wife-beating?