You almost had a point, but you botched it. It wasn't urbanization so much as it was industrialization which devalued and then undermined the work of women.

But as always, it hinged on already present poor attitudes about women from men. After all, any society could have paid female workers equally from the beginning.

Concubines were known accountants and other administrative laborers for their lord back on the day. So, once Industrialization happened, those clerk jobs didn't HAVE to go to men. Women could have been hired and paid compatably. You don't need big brawny muscles to hold a pen and push ink across a page, after all.