I'm not certain what the costs are you are referring to. However I do know that no one wants to be treated like a second class citizen. Most people are for equal pay for equal work and so forth. The only area where there has been some regrets by women in particular is in regard to courtship, dating, and romantic relationships. Chivalry may not be dead but it's on life support.
There was a time when a man pursued a woman with flowers, cards, poems, and paid her compliments. (Today we are looking for women to meet us half way.) No one wants to be accused of sexual harassment or worse, being a stalker. Chivalry always contained some element of sexism..."women are the weaker sex" sort of thing. A lot of women today would rather a strange man NOT open the door for them because they don't want to feel "obligated" to have to thank him. In fact many women don't! They simply walk through as if the door opened up (automatically). lol! Some women are reluctant to smile or say hello to men for fear the man might see it as a sign they want to be picked up. It's gotten to the point where members of both sexes tend to only be kind to strangers they are attracted to or interested in.
Everything comes with a price.In the battle between being treated as "equal" vs "special", equal has won out! My guess is women today are more happier with the (options) they have compared to the women of the 1920s, 30s, 40s, and 50s....etc