> The second part of the problem is societal: women are discouraged from pursuing higher-paying jobs by society. This isn't the fault of the women themselves
I really think that point of view is both wrong and harmful.
It's true that society influences people in various ways. But you're assuming that what men do is the "default", and so if women do it less, they are discouraged.
Instead, looking at it from the women's side, perhaps it is men that are overly encouraged to do certain things. For example, men are highly overrepresented in prisons compared to women, and that's not good.
That might be an extreme example, but the fact is that many studies show that men care more about careers that make money, while women care more about making a positive difference in the world (obviously, both only on average). Given that, perhaps society pushes men too much towards tech and finance and so forth. It would be better if we nudged men instead towards nurturing professions, where you help people every day, like nursing or teaching.
In other words, society influences both genders in various ways. Any difference could be either women pushed one way or men pulled the other.