Oddly, many of the polyamorous people I know don't actually care much if poly marriage is legalized. This is basically because most of them practice hierarchical poly; some people have "primary" relationships and also other relationships, and some of those just end up marrying their primary. Also, group marriages present some difficulties in implementation.
IMO human nature will be the final determinant. We know that same sex relationships are as old as humanity. Despite some rare occasions, previous large scale political structures that were stable were built on heteronormative foundations. However, as the possibilites for stable political structures grew to include the possibilities for more social heterogeneity, a constant minority has become better able to realize its natural expression. Whether or not a polyamorous minority suppressed by current structures exists remains to be seen. I haven't encountered much evidence of it. That said, there's no doubt that many on the hetero/homo sexual spectrum assumed roles that were more hetero than their inclination due to pressure. If anti-polyamorous pressure is lifted, there may be a realization of some sort. But, even if that comes to pass, it's pretty clear that it will be some time in coming.
In a way, Americans have already moved past being a truly monogamy-based society, especially in comparison to social (and political) norms for the country's first century. The compulsory expectation that you will enter marriage with one partner for your life has significantly shifted in the last 50-100 years. Outside of extremely religious communities, it is simply not demanded that you only sleep with one partner and remain with them for the rest of your life. Hookup culture, especially among college-aged people, has become the new norm. Four in 10 children are born to unwed mothers. Divorce and remarriage is common. Around 30% of husbands and 20% of wives have had extramarital affairs. About 4%-9% of Americans are currently in open marriages (for comparison, LGBT people make up only about 4% of the US population). Monogamy is what we say we expect, but we don't actually police sexual relationships in a way that enforces that as a social structure anymore.
I agree that just as SSR have been suppressed, monogamy has likely been enforced beyond a level that it would exist at without the pressure. But even so, it doesn't necessarily follow that polyamorous unions are an alternative to monogamy that people are seeking. Even an open marriage is quite different from a polygamous one.
I think polygamy should be legal. Polyamory is impossible to stop, so it's a non-issue.
The communities that practice polygyny are doing it right now, regardless of the law. It can be pretty brutal, but so can monogamous marriages, and they should be treated the same. Domestic violence should be (and is) illegal, and no one should be forced into marriage against their will. In practice, of course, people are going to be indoctrinated from a young age, misled, and pushed into marriage (polygamous or not), and we should find ways to stop that. Banning certain types of marriage is an ineffectual method, because polyamory is unenforceable.
It's a little different. Men and women are born at a 50/50 split. If married men in a town each marry 3 women, that means only 1/3 of the men can get married. This creates intense competition among males and is a contributor to the abuse against boys we often hear about as men in power try to drive out competition. It also lends itself to these child brides as there aren't any age appropriate women left. Not exactly the hallmarks of a healthy society. I go back and forth. I believe in religious freedom, but preventing a society like that seems important too.