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.
I know patients who bring a dozen roses to the doctor's office. And, boy, the next visit, nobody forgets that. You come in and hey - 'Here's the lady who brought the roses' vs. 'Here's the lung cancer.'
It is amazing that people who think we cannot afford to pay for doctors, hospitals, and medication somehow think that we can afford to pay for doctors, hospitals, medication and a government bureaucracy to administer it.
You treat a lady like a dame, and a dame like a lady.