Mixed workplaces are more problematic. Most industries were almost exclusively single sex and things worked well without HR
If you were right, literary works like Nikolai Gogol's "The overcoat" wouldn't exist. https://en.wikipedia.org/wiki/The_Overcoat
HR was invented because workplaces didn't work well, and that was about 50 years before mixed workplaces were common. You're just projecting your biases and ignoring the facts.