It's a shame that this even has to be a topic, and worse that it isn't going away :C
I recently went on a solo month-long trip to Hong Kong and Thailand. As a male, I was plenty frightened walking around alone especially at night in a strange place, with all the looks you get from locals. I can't even imagine how nerve wracking that would have been as a female.
I'm a pretty paranoid individual to begin with, always with my eyes and ears open when out and about and the only thing I can really do is to try and transfer those thoughts to the women I know. For instance, never ever walk around at night with headphones in blasting music, male or female, that's just asking for trouble.
I definitely agree women shouldn't be afraid to travel alone. It can be totally safe if safety is made a priority, but that's true for men and women, it's just that much more important for the women.
you should not be afraid of it when you travel to the Americas or Europe but a different continent if the asia because our culture is different from them, but if you are correct preparations are not many things that need to be afraid of
remains to be adventurous friend.