State's Interest in Marriage?

During debate in the Supreme Court, one of the justices made an interesting comment.

JUSTICE GINSBURG: Mr. Clement, the problem is that it would totally thwart the States' decision that there is a marriage between two people, for the Federal government then to come in to say no joint return; no marital deduction; no Social Security benefits; your spouse is very sick, but you can't get leave; people -­ if that set of attributes, one might well ask, what kind of marriage is this?

(I corrected the official transcript, which seemed to have some trouble with Justice Ginsburg's accent)

It is remarkable that Justice Ginsburg's question presupposes that the entire purpose of marriage relates to Federal labor and employment law or federal tax law. The answer to her question is that obviously states have other uses for having state laws including state labor and employment laws and state tax laws, but also for things like adultery, divorce, and other family law issues, and further for marital privilege in state courts.

Moreover, suppose that the whole purpose (from the state's perspective) is to allow people to benefit from Federal benefits?  What is to prevent states from defining marriage as simply living at the same address, to permit roommates to secure federal benefits, regardless of sexual activity or actual marital relationship?

I realize that all this is rather trivial compared to the problem of a society ready to endorse the behavior.  Still, it would be good if there were clear thinking about the issues.

-TurretinFan