This framing ignores the fact that most people who commit crimes like the ones you mention are men. A man encountered in one of those situations alone is a lot more likely to be a threat, so I'm not sure why you'd expect that a woman would try to initiate conversation with him.
? I'm not saying women are supposed to chat up random men. I'm saying of the women I know well, not one has ever cared about the danger non criminal men face in the world. All they talk about is the danger women face.