chess "hotties" and social stereotypes in the ultimate intellectual sport

According to Chess.com,

When Bobby Fischer was in a Japanese jail in 2004 for using a canceled passport, Boris Spassky wrote to President Bush to free Bobby or place him also in jail and supply them with a chess set. Bobby, in a rare display of humor, requested instead the young Russian model Alexandra Kosteniuk, whom they say is as beautiful as the young Elizabeth Taylor.

Alexandra is an International Grandmaster with a Fide rating of 2515.

Kosteniuk’s motto is “beauty and intelligence can go together”.

Kosteniuk is correct, yet female chess players are usually noted for their beauty, and not their brains. Take this contest, where viewers are encouraged to rate the most photogenic women chess players. More than half the women are master level and above, but they are displayed in order of their beauty (as determined by popular vote).

My understanding is that while there is definitely no shortage of professional female chess players, many tournaments and leagues are still separated by gender. This -- despite the fact that chess isn't usually a contact sport. (Yes, I know about chessboxing. I'm not referring to that.)

Finally, in Checkmate: The role of social stereotypes in the ultimate intellectual sport, a paper in the European Journal of Psychology, Dr. Anne Maass, et. al., pitted male and female players against one another to examine the role of gender in performance outcomes. In the study, women had a 50% performance decline when made aware they were playing male opponents. I find this interesting, but unsurprising, given the social pressures for women not to confront men in most cultures. If women and girls are socialized to be less confrontational (perhaps even submissive in some cultures) in their interactions with men, then it would likely carry over in competitive and other situations. I'm wondering how culture (religion, nationality, etc.) exacerbates this and if any other studies looked more in-depth at performance outcomes in societies where gender social constructs are especially rigid.

Thanks, Jimmy O.