@M199 So sorry to hear your daughter found herself in this situation and that there weren't any public resources available to her. And I can see why you would now feel that hosts should open themselves to housing for such cases.
But I don't think hosts should necessarily open their doors to someone in such a situation, because it can often be dangerous with someone unknown to you. This is why "safe houses" for women and children escaping domestic abuse- their location is quite secret, there is trained staff, they have security precautions in place, coordinate with local police they can call on if necessary.
While it may not have been a risk with your daughter, as I'm sure you are aware, many abused women leave and then go back to their abusers, are "addicted" to the relationship, or too afraid to cut ties or refuse to communicate their whereabouts to the abuser. In other words, the woman will answer the phone when he calls, tell him where she is (or he somehow manages to find out) or call a friend and say where she is and then the abuser manages to intimidate the friend into giving info, and then a really dangerous situation could arise for the host, who isn't trained to deal with such things.
You said there were no public resources available, but most areas have a crisis line people can call, and I know that at least where I lived in Canada, the person on the other end of the phone can send the police to retreive the woman if she wants that, and take her to a safe house designed for that purpose.