[I]f you are in a polygynous relationship in the developed world you are probably either of Mormon Fundamentalist or Muslim faith, both of which forbid the consumption of alcohol . . . [and] pre-industrial societies with polygyny as the dominant marriage institution consume less alcohol than those with monogamy.
From here (citing Squicciarini, Mara and Jo Swinne “Women or Wine? Monogamy and Alcohol.” AAWE Working Paper No. 75).
One theory is that industrialization favors both alcohol consumption and monogamy, but early LDS society seems a poor fit to this model, and both widespread use of alcohol and the demise of polygny far pre-date industrialization.
Polygyny virtually vanished in the West by the time of the late Roman empire. Alcohol consumption was rampant and exaulted in the West by the time that the Myceneans took over in Greece, if not earlier, a millenium or more earlier. The Byzantines had polygny at some some level pretty much until it fell, as did the Ottomans that followed.
Judaism appears to been polygynous at least through the early Iron Age (ca. 1000 BCE), but had probably ceased to be by the dawn of the Rabbinic period, ca. 70 CE, and has accepted alcohol consumption to some extent, although not necessarily to excess, for all of its history.
Perhaps the more relevant point is that a prohibition on alcohol consumption is a measure of how powerful a grip a religion has on its participants, and hence, how much capacity it has also to influence marital practices of its members.