yeah except perhaps industries women go into pay less because women are in them?
to wit: computer programming used to be "a womans job," then it changed to "a mans job" and pay rose. teachers are seen as womens work, and pay poorly. so too are nurses. i think i also heard tell that russian science was considered "womans work" and paid less than western scientists? i'm not so sure about that one.
point is: "women go into jobs that pay less!" is not the end. why do women go into those jobs, and why do they pay less?
I did point out one reason that female industries are paid less is that employers of women are often lumped with subsidizing childcare arrangements in one way or another (often enforced by laws which are intended to help women, or at least make politicians seem women-friendly), and to not be "discriminatory" they have to spread those costs across their whole workforce. Which means that even women without children are paying for other women's kids. Women also choose jobs where taking leave isn't as big a problem, and doesn't hurt your pay rate as much. e.g. taking a year off from a factory isn't going to hurt as much as other careers. And women also choose jobs with flexible hours. All of these things are to do with the fact that women are planning ahead for having kids one day. In addition, "gender neutral" parental leave is almost all taken by mothers, not fathers, and it's not the
woman's employer who is at fault there - the blame more lies with the
father's employer if at all, for not fostering a culture of men taking family leave.
Additionally, when you do a more detailed breakdown of the gender pay gap, it's almost 100% concentrated in women with kids.
Any "helpful" policy that makes life easier for working mothers is nice, because it's the "right thing to do", but it does cause the birth rate to increase as well, which pushes more women into the category that has the higher gender gap. All of that just reinforces the existing gender gap. Only Sweden is ahead of the curve here, with policies encouraging dads to take a share of the parental leave.