We can go back and forth about this. I'll counter with garbage collectors (chiefly men) having to deal with liquid trash, you'll talk about female secretaries having to deal with harassment, I'll talk about emergency frontliners having to deal with the worst of society, and so on.

And we see the similarity here: they're all relatively low-wage jobs.

The comparison here shouldn't be between high-paid jobs (doctor) and low-paid ones (nurse), rather between low-paid jobs and other low-paid jobs.

The bottom line is that those with lower-wage jobs will be the ones having to deal with the worse things, but generally-speaking women tend to take up the less dangerous, more comfortable low-wage jobs. Think teachers, nurses, secretaries against soldiers, police officers, construction workers.