Historically, polygamy has existed in many societies, much more so than gay marriage, but the logic behind them was socio-economic in most cases. To take Muhammad's case, his main reasons for contracting additional marriages tended to be either creating closer ties to the family of those women, or charity towards widows of fallen comrades who would be hard-pressed to feed themselves and their children without income. Other reasons included being able to share the workload of the household among several women, factors of prestige, and so on. But polygamous marriages between three or more people who did so just because they all loved each other and wanted to go through life together... not so much.

Of course, the evolution in marriage in general that has made gay marriage more relevant and more of an issue now than it used to be - i.e., the shift, in the West at least, from an institution that was at least to a large extent socio-economic to one that is predominantly romantic - also might make this new kind of polygamy, the truly polyamorous kind, more relevant. How many of those relationships are there, though? I would think even today, and even in the West, polygamy if legal would primarily be practiced in the traditional way and for the traditional reasons, either among radical Mormon sects, or among conservative Muslims from countries like Saudi Arabia, like in your example. And I'm not convinced that that's something that should be encouraged.

Which, incidentally, means your "I'm not asking opponents of gay marriage because I already know what they'd say" is not quite accurate - it's a small minority of conservatives that would favour polygamy, and almost exclusively those belonging to a few specific religions or denominations, but it's still there and from what I can see, it's probably more numerous than the progressives who want it because they're in a genuinely polyamorous relationship.

I have issues with this new-style polygamy for practical reasons too, obviously - it's hard to see how they could work all that out.