Full disclosure: I admit to being more than a little irritated by that smug, self-centered husband Kody the few times I have watched it. (The things I do for my students.) Dude is driving a two-seat Lexus convertible while his wives are making do with broke-down Suburban things. But, except for those gosh-darn pesky feelings that the wives, occasionally, allow themselves to feel but then quickly tamp down; they are all so gosh-darn happy. Get the point?
Here goes (and feel free to correct me when I am wrong. I probably am.)
Polygyny has some interesting consequences for a society. Since male/female ratios tend to be about 50/50 in the world when left to "natural" forces. (Edited for clarification: interesting aside: the full complexities of human sex ratios still have some mysteries to be uncovered.) When one man marries say 4 wives, then three men, theoretically, do without. If this is a repeated pattern in a society this tends to drive up the marriage age for men--they have to wait to get married and drives down the marriage age for women--they are married off young because they are in short supply and, thus, desirable. Society-wide over time you get a pattern of older men with multiple wives and younger men without any wives. This is what you see with the Maasai, for example. And some men will, always do without. Powerful older men end up dominating the society and women (girls) get apportioned to them.
The societal problem that often results (and all societies have problems that they deal with because of their structural organization; one of ours, for example is the race/poverty issue) is a large number of young men who can, potentially, cause trouble for their elders. After all, the women may find them more attractive than their elder husbands. The solution of the Maasai for many years was to send the young men away to do other things; cattle raiding/warfare, for example. This used to work better for them in the past but now that you can't go out to kill a lion because of that whole endangered species thing, there are issues. Thank goodness, there are jobs available for Maasai moran with American Express.
So, anyone else facing questions about the show? Are you going with the "its all good" philosophy?