Don't discount sexual frustration as a source of increased tendency to violence. Polygamy doesn't just mean that some men can have multiple wives. It also means that some young and poor males have no chance to marry, because there aren't enough women to go around.
That's a misunderstanding of how polygamy works in those societies who practice polygamy. This we can put in the category of not a problem. In reality it's strictly policed through customs rather than law. So even though a man can legally have a bunch of wives there´s quite a few hoops to jump through. In practice nearly all Muslim men can only have one wife. Only tribal chiefs and aristocrats have more than one wife. Typically Muslim women insist upon an added clause to their marriage contract that prohibits their husband from getting a second wife. It's a checkbox to check. It's standard.
There are legal restrictions worth considering if you do want more than one wife, even when you're allowed to. Basically, unless you are pretty wealthy, ie rich, don't even bother. You need to provide for them amply and make sure they have identical standards of living. Or she can divorce her husband. For example Saudi Arabia. Divorce law in Saudi Arabia makes it hard for women to divorce their husband. But if she manages to do that then he is bound by law, for the rest of his and her life, to provide for her. Even though they are divorced. That's something to consider before getting a second wife. All this requires ample funds.
So Islamic law, albeit medieval and retarded, isn't pure evil. A divorced man has zero rights over his ex-wife. Only duties. So a man does best to avoid that situation at all cost. Which means not giving her any reason to be jealous of his other wives.
Every second wife around means a man without a wife. Just because it's a small percent doesn't mean it's not a problem.
I strongly suspect sex-selective behaviors have more to do with the problem than polygamy, though.