If women refused to participate in a women's championship it would cease to have any public meaning. I mean sure some 1500 woman could be crowned the official world champion but nobody would recognize it as valid. Why don't most women chess players do this? Well women's events including but not limited to the women's championship have tremendous economic value. Hou Yifan with a peak rating of 2639 would not be invited to the Tata Steel A group if she was a guy. She would get invites to Chinese tournaments and would not be able to make a living as a player (so she would either improve or be a part-timer). Koneru Humpy would be in even worse shape as far as career viability.
AS to what causes the lack of women who would be able to compete here are some preliminary thoughts--
1. There are far more serious male chess players than female. I have seen quotes that less then 5% of tournament players are female. I don't know if that is accurate as it seems a little high in my experience but certainly 85% or more are men. There are tremendously long arguments on here (search Title IX discussions) that men participate in higher levels in a large variety of competitive endeavors so it may be that this is a sex linked characteristic which cuts across many fields.
2. Take as a given (it is not but the point may stand regardless) that intelligence is correlated to success in chess. Then take as a given that women and men ave the same standard IQ scores (which they do but that is because the tests are designed to achieve this, this stuff is complicated). Men still perform better in spatial relations and mental rotation sub-test scores which are exactly the area that would be important for the pattern recognition and problem solving imoportant in chess.
3. Even if men and women have the same IQ that does not mean the distribution is the same. Men as a gender seem to have a much wider distribution with many more extremely intelligent males then females. Epidemiological studies also show the incidence of intellectual disability is higher in males than females throughout the world. This wider distribution is seen in other traits as well where men display much great rates of aggression, criminality, and other traits, so that even if the averages were the same in traits related to chess the players at the top may still end up being overwhelming male. Part of that may be a sex based differential in competitiveness (or OCD or perfectionistic tendencies if you want to state it less positively) which leads to the participation numbers listed above.
None of that means that a women couldn't be highest ranked or world champion or that they couldn't competitive on a level playing field if the chess world was structured differently but it is just not so easy to say there shouldn't be a gender based difference. Anyway those are just a preliminary stab at something I think is an interesting discussion. If none of that makes sense it is doubtlessly because I am on heavy narcotics at the moment which is why I am writing this at 3 AM. Please forgive the misspellings.