I think it may have something to do with limiting violence.

I'm trying to remember the reference (it might be Hanson or possibly the book the Red Queen Hypothesis - if I remember I'll post it) but a vast majority of violence is over access to women, at least in primitive societies. Obviously mongamy means that the largest number of males get access to a female, thereby reducing losses in violent competition to females. I think this would certainly explain why rich societies tend to be monogamous - less destructive waste.

Additionally I can imagine societies with high levels of polygyny (think emperors with giant harems) could be extremely unstable due to sexual jealousy, but that's mere speculation.

Apologies if this has already been posted - I was late to this thread and there's an unmanageable number of comments to search through.