I think prohibition did, in some way, improve the lot of women in the United States. During prohibition, more women were starting to be vocal. There were some against prohibition, some for it, and some speaking out about the crime and corruption due to prohibition being passed. It gave them a spotlight.
Everyone knows that although Prohibition existed at the time, almost anyone who wanted to buy alcohol could. And in fact what was banned actually became more desirable and involved contact with shady underground characters. So while technically there should have been less domestic abuse, there very well may not have been if the alcohol was around.
Prohibition did not improve the lot of women in the United States. Although the ban of alcohol in the United States theoretically would have improved the lives of women by limiting the occurrence of domestic abuse by alcoholic husbands, in reality prohibition did not end the consumption of alcohol, it actually increased the consumption of alcohol through the efforts of mobsters and gangsters.
Prohibition didn't improve anything in the United States, it make everything worse. I think trying to illicit the idea that somehow prohibition is helpful is dangerous to society. Prohibition creates criminals where there once were none. This doesn't help men or women and it doesn't change their social standings either.
I do not believe that Prohibition improved the lives of women in the United States of America. I think that there is no evidence to suggest that the banning of alcohol decades ago was beneficial for women in America. I do think that Prohibition proved that American couldn't live without alcohol.