There aren't more lady songwriters for the same reason that there aren't more lady doctors or lady accountants or lady lawyers; not enough women have the time for careers.
When you have to do all the more crappy jobs before, you appreciate all the good work that comes out of that. There are many girls who immediately have a top model career, and there are lots of models who are doing things that aren't as exciting as doing big campaigns and beautiful magazines.
The sweat of hard work is not to be displayed. It is much more graceful to appear favored by the gods.