That's why we need salary transparency to really address this. There are a lot underpaid men and a lot of overpaid women. Making this into a male vs. female issue does nothing to address the fact that people are underpaid.
I think it would quite quickly turn into yet another source of conflict between employees. The problem with "equal pay" is direct comparisons only work in jobs that are essentially assembly line work, e.g., person A and person B do exactly the same thing every single day, and their output can be measured in exactly the same way, namely how many widgets each person produces in a given time period. Finding a difference…
there are plenty of environments where salaries are known and there is not more conflict than anywhere else. For example Congress staffers' salaries are public, there are huge pay differences for the same position but it sill works.
I think most arguments against transparency are spread by employers to keep the information asymmmwetry.In most markets the party that has more information will have the advantage.