"Women have shown a tendency to favor work life balance over income on average which means if you want to increase female mobility in male dominated jobs you need to increase working conditions for men, like equal entitlements for paternity and maternity leave."

This is very true. Though I'm not sure that any country has equal entitlements for paternity leave... men get less mostly because of the physical difficulty of birth and breastfeeding, but more than is entitled there. It helps if the employer isn't forced to pay for the maternity leave, only keep the job open for when she/he returns. (social benefit). Plus laws that protect parents taking time off for sick children, etc.

In countries where child raising is much more equal between the sexes, however, you still see pay differences tied to career choices. Teachers and nurses (which are often female-dominated) often get paid less than male-dominated career choices with equal education requirements. Even when there is a shortage of nurses and teachers... they still pay less.

And I have no clue what the solution to such things are without simply having a different system to pay folks. For example, some sort of equation that combines experience, amount of education required, stress levels and 'untraditional' worktimes, experience, etc. But I also think this would be pushed against greatly.