It’s not an assumption. It’s been tried since the dawn of time and is the only efficient enough system that works for mankind. Do care to show me a formal study case where this has been proven false. Polygamy is outlawed for the same reason other crimes are outlawed, it hurts people EMOTIONALLY and leads to physical violence in many cases.
What does believing in polygamy mean anyway? I believe we are polygamous by nature too. Not only that we are also violent by nature yet violence is not acceptable in any society for it to function properly and prosper, why should polygamy be treated any differently? Polygamy hurts people as much as physical violence does. Emotional health of human beings is just as important.
We defy nature in many ways, polygamy is just one example. And let’s not forget, polygamy tends to play in men’s favor more than women simply because we are the weaker sex and easily controlled. So if we legalize it, women are likely to become victims of it more than men.