I sympathize with your point and understand your feelings. However, these type of lawsuits (and the associated political agenda) ignore the existence of something called Arbitrage. Not arbitration, arbitrage.
Arbitrage, in a nutshell, is when the price of something is wrong (goods, labor, etc.) somebody will make profit by correcting the mistake in pricing.
If women truly were paid less than men for the same output, under an identical nucleus of operating facts, it would be beneficial for employers to hire as high percentage of women as possible, ideally 100%. Within a decade, all jobs would be held by women, supported by men who’d stay home and do “man’s stuff.”
In reality, every time you attempt to discriminate based on things like race, or gender, as a market participant, you leave money on the table for your competitors to grab. Hence, the free market is the best policeman against discrimination.