Good post - I particularly enjoyed the comparison between women's sport now and how men's sport was.

I think there are a few (not many) great initiatives coming out of sport, which I believe the ATP/WTA tours initiated -

1. Lewes football club are the 1st football (soccer) club to pay men and women the same. Imagine that, the top female footballer being paid the same as Cristiano Ronaldo?
2. Extreme E - The new racing series that has 1 male and 1 female driver in each team. It's a real triumph to see this equality.

I hope, and I'm sure we will see more of this kind of initiative. Like you say, confidence has a lot to do with it from a player's point of view but more importantly, confidence in governing bodies, governments and societies to force through the change which living in the 21st century demands.