Why does it affect men disproportionately less?
I don't even know if we like to find a non-economic reason or if most people simply don't know economics well enough to reason through 2nd and 3rd order economic consequences. Since they can't reason through it they choose simple explanations despite it being wrong. This is the same reason why people used to believe that deities controlled things like the weather and their fortune in life.
The "patriarchy" gets basically the same faith-based treatment as Zeus/Jupiter.
Not even for a minute suggesting that women should not be allowed to work in dangerous environments. Having said that no one wants to subject themselves to dangerous work and it is perhaps slightly easier for women to avoid that.
While not specifically about time, the difference principle in Rawl's Original Position is also relevant. Under that principle, inequality is permissible if it can lead to the worst off being better off than they would if there were equality. This principles presupposes that time is considered when trying to maximize well being for the worst off. If you want to maximize the well being of the worst off in the present, you implement equality right now, but that may be worse for the worst off in the future.
"More Americans died in making stuff for the WW1 than in the actual war, as the conditions of factory work was brutal."
I'm doubtful that this is true for many other countries involved in that war.
The US basically wasn't a major combatant in that war, so it's not a representative country to use as an example. I'm sure it does show that factory conditions were brutal, but it falsely implies that they were more brutal than combat conditions.
People are really smart and they optimise for their own survival. Essentially - decent wage -> better options for partner -> better standard of living. In some countries, like Norway, a teacher makes a decent wage. Not as much as a software engineer, but good enough to support a pretty good lifestyle.
Where in some countries, like India, a stem graduate makes a LOT more money than a teacher. I made more money in my third year as a software engineer, than my father who worked in public sector as a civil engineer with 25+ years of experience. Comparison with non technical workers with stem fields is really lop sided when it comes to earning potential. Plus if you are possibly the first generation which can break out of poverty cycle for your entire family, then that adds another layer of pressure to choose certain fields. Hence men or women tend to choose these fields.
As wealth creation in some of these countries reaches to a point where non stem fields receive similar earning potential, already happening in India, we will see lower number of women opting for these fields as well.
We would really like to find a non economic reason for some of these disparities, like patriarchy, gender discrimination and so on, but it is probably mostly economic.