Not traditionally for nursing mothers.
I remember them from my childhood, when ladies dressed up to go shopping. After a few hours of walking around in heels, wearing a girdle, women wanted a place to sit and rest. Department stores routinely had 'ladies' lounges'. My university campus had a ladies' lounge in the student union (taken out in the 1980s) and many of the women's rooms around campus had a sofa in them. At that time, there weren't enough women who worked there or students who were bringing nursing babies to campus, so that couldn't have been the reason for them. In the department stores, I never saw a woman nursing a baby- it was typically middle-aged women with their feet propped up.
And yes, I've heard the story that it was state law requiring all those sofas, so I don't think it's fair to call someone SS because they'd heard that story, too.