> Society needs both nurses and engineers.

Yes. And if more people want to become engineers, and if becoming an engineer is easier, then engineers will end up getting less money than nurses.

I mean... the more fun a job is, the more people will want to do it despite getting little money, right?

> In addition, women are usually the primary caregiver and disproportionately spend more time doing domestic labour (raising children, taking care of the home) which they are not compensated financially for.

I recall reading some statistics that (in germany) 80% of domestic spending is done by women. Seems about right.

> Women should be paid more for fewer hours in the workplace.

Uh. That's outright discrimination there. Either against men or against childless people.