It was common in 19th-century America to refer to slavery and polygamy as the "twin relics of barbarism." Polygamous societies are seen as patriarchal just by virtue of their being polygamous. After all, who do we think the real driving force behind "two girls for every boy" thinking is, the dudes or the ladies?
This ignores the fact that the real winners of polygamy aren't men as a whole. It's a very small subset of men who receive the increased progeny polygamy offers. And it's women as a whole who see their marriage opportunities improve (assuming a married lady has a veto over her husband's proposed additional marriage, which Aristophanes and William Congreve say they do).
Assume desirable traits are normally distributed among men and women. Assume that a man or a woman receives value equal to the percentile of the population the spouse is in (so a husband with traits better than 99% of the population would bring a value of 99 to his wife). Assume that being a man's nth wife reduces that value by a factor of 1/n. Assume men and women seek to maximize the value they receive from marriage. Then in a monogamous world, the best man marries the best woman, and the worst marries the worst. Spouses are relatively equal, with the only variation coming from any unequal distribution of the sexes (the World Bank estimates 49.584% of the world is female, so generally women would marry slightly above their level and the bottom 1% of men have no marriage partners). But in a polygamous world, around half of all women would prefer to be the second wife of the most-desirable man. This isn't due to patriarchy or sexism or chauvinism, it is due to women seeking their own self interest.
I'm under no illusions: there's some man somewhere that would improve my wife's life if she became his second wife. Statistically speaking, I'm pretty certain. How many men would not be married if women could be polygamous? Given that the current reproduction ratio is four women reproducing for every man who does, I'd say quite a lot of us.
As Adam Gendler writes
Contrary to both traditionalist conservative myth and popular feminist narrative, for most of history patriarchy was not a privilege one benefited from simply by being born male, but a brutal racket in which millions of men destroyed each other and the world around them for the benefit of a fortunate few.At some point in the future women will realize that polygamy is in their interest, and the societal implications will be terrible.