The Romans and Greeks did not have legalised polygamy. I wondered why. As I understand it, the evidence is that polygamy was common in the distant past, and in the Middle East there are references to it (for example, in the Bible, Solomon had like 200 wives and 800 concubines or something like that). So I wondered why not with them.
Monogamy has long been a cultural norm for humanity, because evolutionarily and biologically speaking, it's actually most advantageous for humans to be so. Humans are Extreme K-type reproducers with no mating season, and as such, it was evolutionarily advantageous for early man to ensure the healthy survival of his offspring to stick around. Recent papers in the PNAS have found that contrary to some societal tropes, humans are actually hardwired for monogamy and historically always have been.
Gavrilets and de Waal (2013), 'Monogamy with a Purpose', Proceedings of the National Academy of Sciences 110/38.