To be honest, more women probably
did stay home in 1913 than they do today. It's not that they wanted to, but they simply didn't have as many opportunities as they do now. (Remember, 1913 was at least 8-10 years before the suffragist movement finally succeeded in granting women the vote).
I know I'm generalising here, but to be more specific: upper-class women in 1913 probably had more opportunities to leave the house, if only to visit friends and/or the doctor. They were, however, more restricted by societal expectations of how "a lady should behave". The housework was done for them by servants.
Lower-class women in 1913, OTOH, had no such opportunities. They might leave the house to go to the market, but since they had less money, they couldn't afford as many servants, and therefore had to do more of the housework.
Somewhere in between is the middle class, i.e. those who could afford to pay for more servants, and strived to the life of the upper-classes, but couldn't afford to. It's difficult to know how much freedom women there had, but probably not much more than women in lower-class houses. They were probably free to go dancing with their husbands when a special dance was being held, but not much more than that.
Unwed women, of course, were a completely different kettle of fish (and no, of course I'm not being literal here).

They were constantly watched and chaperoned
everywhere. A young, unmarried woman in a middle- or upper-class household didn't have anywhere near the same freedoms as she does today. She was not free to, for instance, dance with just any man she fancied. There were rules and codes that are absent today.
(And yes, I know I'm probably preaching to the choir again.

But history is one of my specialties, as I'm sure you know!)