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.