I think this post is skipping the crucial factor in all this. It's not about children--at least not directly. It's about risk. Several years ago I read an article that analyzed the work preferences of the genders. It demonstrably showed that: - Men are more likely to do riskier jobs; - Men are more likely to travel further to work (including internationally); - Women tend to choose that are closer to home. Basically…
"Nowadays there aren't any barriers preventing women from taking these paths (quite the opposite, actually). It's simply that less women choose these routes." Begging the question. As you point out, there are no laws or physical barriers preventing women in the US from doing just about anything, so their heavy relative underrepresentation means by definition they're choosing not to. The question is: why not? Choices…
Conversely, men are less likely to attend college, are more likely to be unemployed, are more likely be injured in the course of employment, are more likely to be the victim of a violent crime, are more likely to be incarcerated, etc etc, every single day.
Just because there are no laws preventing women from doing something does not mean that the playing field is equal.
Just because there are inequities in one direction does not mean that there aren't also inequities in the opposite direction.