Then I'm not sure exactly where you're disagreeing.
Yes, some men may pass her up on the basis that most attractive or otherwise women do indeed have hair and why settle for the one who doesn't?
But as you also agree, she wouldn't face many rejections due to simple male "thirst". It is that thirst that means even if a woman possess "undesirable" characteristics, she will still have many potential partners.
We cannot say the same for men with her condition.
@lemoncloak
Seems that your response is mostly the "personality" cope, but shookwun is 100% correct. "Game" doesn't matter if someone finds you attractive.
Negative personality traits are spun as being postive traits on attractive people; especially men.
Average: "Omg he's sooo creepy. He never says anything!"
Hot: "Omg he's sooo shy it's so adorable!"
Average: "What an a**h**, he has no regard for anyone but himself!"
Hot: "He's a strong, assertive man who isn't afraid to take what he wants!"
These and more are double-standard quotes I have personally heard come out of women's mouths since at least high school.