I have seen a lot of women in domestic violence situations. Trying to understand why women stay is not wrong, but you have to open to hearing their reasoning. Some reasoning is more understandable than others. Mostly, I think a lot of women are scared to leave and don't see a opportunity to do so. If the man is really possessive and controlling, she may not have money of her own or a safe place to go. If she has young children, then that complicates the situation even more.
I have done volunteer work at women's organizations, and I have seen plenty women try to save money and research a safe place to go. They tended to plan for a few months before actually taking the steps to get out for good. The safest way to get out, is to leave when he isn't home, and try to make sure he will not be able to follow or find you.
That takes a lot of planning and reorganizing your life. You have to get a different phone, change numbers, find a lawyer, etc., It's super stressful, and when a child is involved, it's even more stressful and scary. Some women stay because they are afraid of leaving. Some wait till the children are older or adults to not disrupt the child's life, but that can be terrible on the kid growing up in a violent home. Some physically abusive men turn into manipulative, weak men as a they age. They may not hit as much or as hard, but they are still controlling, selfish, and emotionally abusive.
I don't think a woman could be happy with an abusive men at any stage of his life, and I have heard a lot of stories from all kinds of women and have seen it for myself.