This is all a moot point.
There are not laws or restrictions against women playing in professional sports. The truth is just that there are not any women out there who could possibly hope to compete with men at that high of a level. I'm talking about "real" sports (this will probably start arguments lol), not golf, racecar driving, table tennis etc. The only exception that comes to mind is Billie Jean King in tennis. But today the gap has widened considerably between men and women with the onset of steroids and other supplements.
Is it not fair that women don't then have their own leagues? I think it's perfectly fair. Sports are a business just like any other business, and the product they sell has to be a good one. Women are, from that perspective, not as good of a product, so a lot of times there is no market for professional women leagues.
Yet those leagues still exist.
The WNBA has been nothing but a giant sinkhole of money. Women's college sports are pretty much never cost effective. Instead taking money from the more expensive profitable men's programs... (and often complain that they don't get equal money and scholarships.)
The free market doesn't come in because people think that seregation is being fair for some reason. Seperate but equal so to speak. (Or seperate but not equal.)
Yes, those leagues still do exist. But like you said, most of them only exist because they are "allowed" to exist. My point was that women playing sports are not as good of a product from an entertainment perspective because men are so much more athletically superior, it makes for more compelling competition. With the exception of mostly tennis and maybe the WNBA, most women sports would not last long if they weren't allowed to exist as they do.
On an aside, people have always complained about sexism in sports, it seems. So the solution is Title IX, which requires high schools and colleges to have an equal, or greater, number of women's sports teams to men's teams. So how exactly does it make things "equal" when most programs now offer more women's sports teams than men's? Doesn't that turn the discrimination on its head?