That isn't true. Women's hair has been culturally tied to their femininity for so long that women would no longer think they would be treated as real women if they started to bald, which did sometimes happen. This has changed somewhat in modern times, but for much of history it was the case. I can't compare it to gender disphoria as experienced by trans people because I've never been a balding woman or trans. But those are both experiences stemming from a similar root cause, balding as a sign of non-femininity.