I chose my words intentionally for the context of the post. I said ‘often’ not ‘universally’. The post is asking about social acceptance and I was pointing out that polygamy already is socially acceptable in some cultures and where that’s true it is often in the form of patriarchal hierarchy.
Also polygamy by definition is a hierarchy because there is one primary partner with many partners/spouses, but those partners don’t have the same freedom to take on other partners. If they did, then that is called polyamory. Polyamory may or may not have hierarchy depending on the structure, polygamy has to have hierarchy.