Perhaps the issue is also the cost of childcare. Why go to work when most of your wage will go to someone else looking after your child? Yes, there should be better paternity leave programs, but in saying that, it's still the woman who has to carry the child for nine months, then recover afterwards, not much we can do about that. There are also male-dominated fields in which people are also paid poorly for the amount of work they do such as chefs and meat-workers.
In reference to your point about senior positions and management, I'd argue that this would be a bit more difficult to do if you're part-time. I suppose you have to be fortunate enough to have others who can help look after your child when you're at work.
I don't really disagree with your second paragraph, sexism in media is obviously there. For instance, female newsreaders seem to have more make-up caked on them than a bloody escort. One thing that personally pisses me off is the music industry. We've gone backwards in the last 20 years. Shirley Manson and Courtney Love didn't need to parade around half naked (maybe mentioning Love here is futile), to sell records. Not every music video needed women grinding half naked all over the place. Now, we have huge hacks such as Katy Perry, Rhinna and to a lesser extent Taylor Swift, who are average, and often release ■■■■ for brains music. However, they get the cans out and in roll the dollars. In terms of walking the street, I think there's a number of mitigating factors there. Women are physically weaker, so unfortunately we'll always be a target for opportunists, and that includes female attackers also.
Some interesting points raised in this video.