Who do you think was enforcing these stereotypes? Pushing the narrative that men are strong and can work and women are weak and should stay at home? Who had literally all of the power in the early 1900s? Men. Men were the ones who made all of the advertising showing strong men and weak women, they were the ones making the laws that oppressed women, they were the ones speaking to congregations in church, telling people that the bible says men are the heads of their households and bear all the responsibility while wives are there to be subservient. Like, men created and upheld these standards. Why are you putting it just on the women to break down barriers? Where were the men fighting against the draft (in the 1910s, no major movement held), fighting for the right to have women in the workforce so that they didn't have as much financial responsibility, fighting for the right to stay home and take care of their children if they wanted to? Seriously, why do women have to fight to gain basic civil liberties AND fight for to change societal views of women AND fight for the change of societal views of men? They couldn't focus on literally every societal issue, maybe if the men of the time cared that much about their own equality they would've created a movement. But they didn't. Because the status quo let them remain in power over ~50% of the population. Why in the world would they fight for change?

Not all women had families to go back to or ones that would be accepting of a divorcee? Men had the financial and societal power (they wouldn't be viewed nearly as poorly as a divorced woman) to leave abusive wives.

Also, it is much easier to gain civil liberties, like the right to vote, than it is to change entire views that society holds. Women needed the right to vote to enact any of the change you're demanding that they divided their attention between. How could they possibly have fought to be included in the draft if they couldn't elect legislators who wanted to include women? They couldn't call up their local congressman and demand action if they didn't have the ability to say "hey I'm not going to vote for you if you're against women in the military". Women gaining the right to vote was essential to even have a voice in American society.