Capitalism is unfair. But if you have capitalism, of course you'll have a pay gap. If you want communism, just say so.
I had worked at a bike repair (and sale) shop. Had the same job title as all the other mechanics. A few top mechanics had about 50% higher pays. There were two women, with the same job title, but they didn't (want to) do any wrenching. Good workers as well, but they were doing the sales and customer talking. When I learned how much the "top" guys get paid, as well as which one among them got the biggest pay, didn't have any complaints. If anyone had asked me who I'd pay the most and, of all those people, who I would first pick for the job - those were the highest paid ones. If anyone did a pay review - yes, women were paid less. They were also not the one's coming in for overtime, weekend rushes etc, since they wanted to spend more time with their kids. It is cruel, unfair - capitalism always is. But I don't think it has much to do with gender.
BTW, pretty soon after having arrived there, the top guys would use my name as an example how it should be done. However, I left relatively quickly, having realised there's not much left to learn and opened my own shop. So far so good. If I had stayed there, I'd have asked for a higher pay. When hiring a mechanic, IMO it would be stupid to disregard a woman, or pay her less and have her leave, just because she's a woman. My main criteria would be the quality of work, attention to details, good "diplomacy" with the (troublesome) customers and commitment. This last thing is the main difference IMO. Women are probably not as crazy as men and most of them put family before the career.
All those studies never seem to ask the workers being studied what they thing of the pays. Same goes for managers, of course. Do those, less paid female workers/managers thing they deserve to be paid as high as the top paid workers/managers?
The greatest inequality is not between genders, but between classes. But you can't complain about that AND live in a capitalist country. It's like complaining about the heat in Africa.