None of the 85% of cultures that preferred polygamy were competitive economically with the dominant Western monogamous cultures over the past couple of centuries.
None, that is, except Islam. Yes, Islam declined over the last few centuries, but how much of it might be attributed to its preference for polygamy, and how much to other factors like, say, Mongolian invasions which barely touched the Western world but destroyed most of the Islamic one twice. Or accidental discovery of Americas (which is doubly funny because it was enabled by Columbus' gross miscalculation: he thought that Japan was only about 5000km westward from Canary Islands).
So just accept that is for the most part won't be a concrete science.
I do. This still does not mean it should be allowed free speculation. History is in much worse situation as what it studies is by definition non-replicable, and even approximating contemporary statistics and cross cultural studies which are available to evopsych (or would be available if they knew how to do it) are out of the question. So it's in fact only explanations of any available evidence. Yet, historians show much more of scholarly discipline than evolutionary psychologists do.
Most of the evopsych research I read appears to do the thing backwards: assume the answer (it must be an evolutionary adaptation) and try hard to support it with whatever excuse at evidence they can come at and speculation. Outside of evopsych (and Continental philosophy, maybe something else) a respectable scholar should first look for evidence against his hypothesis, then for alternative hypotheses and only failing that tentatively treat his hypothesis as confirmed. And never be ashamed of admitting ignorance (yes, I know, easier said than done, publish or perish and all this stuff.)
I sense there is a decadence associated with the new fondled idea of polygamy for Western culture. We are importing the barbarians again, repeating the fall of Rome.
There are perhaps more theories of what caused the fall of Rome than bad evopsych research papers out there ;) Let's not go there, at least now.