Bar stools were not popular until the Prohibition era. Before that men stood at the bar and drank (belly up to the bar) . Ladies were expected to sit at the tables provided. In some states this was law - no ladies at the bar. In the above postcard of the Cozy cabin you will notice there are no bar stools at the bar.
Enter the prohibition era where speakeasys existed and since they were illegal anyway laws about women at the bar were ignored. In order to make it easy for the women, stools were provided at the bar for them to sit instead of stand and so bar stools became popular for men and women.