Basically proving my point. Very few women in top chess. Currently there are 0 women in top 100 chess players. Only 3 women were ever in the top 100 chess players. And chess is not even a game where men have a natural advantage like in almost all of the physical sports.
I don't deny that there are very few women in top chess, but that wasn't your point. You said it would end up being all men at all the skill rating levels, which is not true. Take chess as an example: there are a lot more women at around 1500 elo than at 2500 elo. So if you host an intermediate-level tournament just for players around 1500 elo, plenty of women will participate.