Historically, monogamy has served many different purposes. Some of those purposes are now obsolete. For example, one major purpose of monogamy historically was to let men know which children were genetically theirs. Nowadays we have paternity tests that can establish this without monogamy. But monogamy continues to serve other purposes that are not obsolete. If practiced honestly, monogamy is helpful for preventing STD transmission. Monogamy can create a different emotional dynamic in a relationship, which may either increase or decrease the stability of the relationship, depending on the relationship needs of the individual people. Many people seem to feel that monogamy provides a greater sense of security, possibly at the expense of some loss of excitement. These assertions are debatable; monogamy means different things to different people. But the alternatives to monogamy tend to look significantly different in modern, liberal cultures or subcultures than in ancient, conservative ones.
Modern, liberal polyamory encompasses many different forms of plural relationships, but relationships approximating polygyny do not appear to me to be an especially common form. The most common form I see is more along the lines of "free love," with everyone in the relationship considered free to form relationships with anyone else they want to, which does not appear to lend itself to creating an underclass of men who can't find spouses. I'm not sure, though, how many of these sorts of poly people would actually want to get married; it appears to me that for many of them, an absence of formal commitment is part of the appeal of polyamory. But this could also have been said of some gay people, and I think the question of how many polyamorous people actually want to get married should not be considered relevant to the question of what right we have to deprive polyamorous people who do want to marry from doing so.
Granting legal recognition to plural marriages is much more complicated than granting legal recognition to same-sex marriages, because plural marriages raise a lot more issues that aren't addressed in existing marriage law, that we would have to figure out how to address. Just to name a few: Should married people need their spouses' permission to marry again? What should be the default legal relationship, if any, that your spouses' spouses should be considered to have with you for purposes such as inheritance and medical decision-making, in the absence of a will or a living will? You cannot be compelled to testify in court against your own spouse; should it be possible to compel you to testify against your spouse's spouse? Should the spousal Social Security benefits of a person with multiple spouses be divided evenly among the spouses and thus reduced from the amount that a monogamous person's one spouse would receive?
No movement for legal recognition of plural marriages is likely to be able to gather much momentum until a fairly clear consensus is formed about how to answer these sorts of questions. How can people decide to enthusiastically fight for something until they have a fairly clear idea of what the thing they're fighting for is likely to look like? So this is a conversation that poly people need to start having, if poly people care about marriage rights. And the way in which poly people decide to answer these sorts of questions can help either validate or address and resolve Jonathan Rauch's concerns.
Personally, having been deprived for gender-based reasons of the right to marry, I am extremely uncomfortable with the idea of depriving anyone of the right to marry for numbers-based reasons. I am, I suppose, a big-government liberal: I tend to think that government regulation is valuable. Of course, the government can and often does regulate many things badly, and the government's previous restriction of marriage to opposite-sex couples was an example of the government regulating marriage badly. (Also of course, I am not advocating rushing people into marriage against their will; I am advocating that people should be allowed to choose when and whether to invite the government to regulate their relationships.) Still, I do not think that a deregulated, anarchist appoarch to marriage is ideal. Government regulation helps mediate the division of assets in hostile divorces and hostile inheritance situations. Government regulation helps homemakers who've sacrificed their career prospects for their spouses' sakes receive some compensation. Government regulation helps, in general, to somewhat protect the interests of the most vulnerable people whose interests might be more thoroughly trampled on in the absence of government regulation. So I would really like to see the poly community take an interest in pushing for marriage rights and deciding on what those marriage rights should look like.
But I am not poly, so I am not in a good position to lead this discussion. I just want to say that I hope some good leaders show up who do start this discussion soon, because if the poly community sorts out what it wants and presents a clear vision of what poly marriage rights should look like, I hope to be able to support them.