I kind of agree with most of what you wrote though as you said, your evidence is anecdotal and sometimes you are a little bit on a thin ice with your cheerleaders observationsI don't think so. I mean women's football gets supported in many countries really hard, like in Germany, where every bigger tournament gets shown. Every league game is at least on ES player. Every club has women's teams. In schools football for girls gets encouraged, there are special training camps for girls during the holidays and so on... the public broadcaster and media make a big from the main events... and it does grow, it does find its viewers and players. But it's nowhere, absolutely nowhere, when compared to men's football. I saw it at my son's primary school where almost every boy played football, and almost none of the girls - but the cheerleader team, full of girls, couldn't take more members, they were full.
And even if girls want to play, more and more do, the viewers are not really there... they will watch a match of the national team, because, women or men, it's still Germany, and they identify with Germany. But there are very, very few people who regularly watch women's club football.
I'm not advocating it should be so, absolutely not. To me, the main problem remains something that I found so shocking about readers: Girls read books with male main characters and are okay with it. Boys want books with male protagonists. And fact: sports viewers are overwhelmingly men, unless it's a big partylike event, then more women are watching. They obviously identify better with men.
Another important aspect: in the families it's still mostly men who do sports. One of the first questions whenever my son meets a new adult is "and which sport do you do?" I don't think it's totally the same for girls. And while men usually continue their (often on a low level competitive sport) when they have a family, the only sport that women often do then is fitness and jogging - to keep fit, to have a nice figure and to get away from the stress of the family, to do something for themselves, so they don't take the kids with them when they do it - unlike the men, who often take at least their sons, (more and more often their girls, too) with them. (It's different if the mothers are very sportive and competitive themselves, but often they simply aren't.) So the children see: men: sports, women: only fitness.
So, most of this aspect is anecdotal, but I still think it would be confirmed statistically. Women do less sport competitively. There are nonetheless enough girls who (often grown up in very sportive families) do sport competitions, but the other consequence is that they are less inclined to watch pro sport because they don't have a connection.
So, overall, what I want to say, basically: It's not that easy. Women's sport is growing, but just because you have a major event for them and it gets shown on tv, that doesn't mean it does have a huge amount of viewers. And while women's pro sport grows, among the young less people watch pro sports in general regularly...
I think a lot should be done to make it easier for women who want a sportive career to make that possible. They should be encouraged. In cycling for instance a strong U23 class and more races for instance would help. Money support for 16-22 year olds who are on the edge of deciding what to do would help. You can still start your studies at age 22 and be successful, I don't think the lessons you learn in competitive sport at the time are wasted. Those are the things I would think about; support the ones who are on the edge, and at a younger age: the ones who are curious but don't really dare because they think it's a boy thing. Make the races more demanding and don't treat the girls and women like "that's not for you anyway, you aren't strong enough".
But forcing gender equality from above when there is no real request for it (for now at least), is not the right way I think.
Hopefully there are still enough teams and people who are interested in forming good women's teams, hopefully with female DSs and CEOs as well, and hopefully women's cycling will grow and get better.
I do not, however, believe that general lack of interest of women for watching sports (or doing sports) is the reason for the gap we have in cycling. Take a look at some other sports: tennis, alpine skiing, volleyball. These sports do not have any particular properties that would make them stand out as "more suitable for women" yet they are very popular - maybe not completely equal to mens' editions yet, but the ratio in popularity is much more equal than in cycling.
It would be interesting to study what made the above mentioned sports more equally distributed between men and women and if there are any lessons learned that could be applied to cycling...