If recognizing marriage is left up to the individual States polygamy will flourish.
Some States allow cousins to marry. For example, California. On the other hand Texas does not so if a California couple, married cousins, move to Texas both would be permitted to re-marry without getting a divorce.
Things would get even more complicated if one decided to divorce. For example, let’s say John marries his cousin Mary in California. Then John and Mary move to Texas and John marries Carol. Mary decides to file for divorce. If she files in California would she be entitled to half the house in Texas?
Of course, if Mitty gets elected he could change the Defense of Marriage Act to a more Mormon view.

Then John and Mary and Carol could live happily ever-after. Also, with a little further tweeking of DOMA, should Mary feel cheated by John having two wives, John could seek a bi-sexual lover and marry him.
Let’s call him Bill. Bill could then be a wife to John and a quasi-husband to Mary. Then we’d have John with Mary and Carol and Bill. Mary would have John and Bill. Bill would have Mary and John.
Should Carol feel she’s getting the short end of the stick, in a manner of speaking, perhaps she and Mary, by exploring their lesbianism, could be the answer.
I'm sure no one would want to add the possibility of 50 different definitions of marriage by allowing individual States to have authority so when it comes to marriage it looks like Mitt's the man.