Fear plays a role in helping people to assess danger, and in making decisions related to your survival and well being. Neither of these things require a fear response though. The article mentions that the woman might have found herself in dangerous situations more often due to her inability to fear, but at best this means that fear might be a useful addition to our ability to assess danger.
It seems to me that the vast majority of situations that are dangerous are either a) obviously so, or b) the opposite. In obviously dangerous situations, you should be able to pick up on the danger by common sense and act accordingly (I don't feel fear every time I cross the street, but I also don't step out in front of cars). In situations where the danger element is very hidden away, it's unlikely you'd get a fear response anyway, since your intuition is only as good as its input.
That leaves a third category, that for which the danger is non-obvious, but fear gives us an evolved intuitive-response to be wary. My argument would be that this is a small and constantly shrinking class of situations, because the environment most of us find ourselves in is so strikingly different than the one in which we evolved. You might have an evolved, intuitive fear response to the sound of a lion's roar, but this does no good whatsoever for most people in the world. So most of the dangerous situations we actually encounter, we deal with using reason and learned behavior rather than fear instinct.
That's my stance anyway. The only area in which I can see a concrete use for fear is its ability to stimulate a very quick flight reaction in certain dangerous situations. That is, things that you need to react to before you have time to think them through. Again, less common in the modern western world, but it does put at least one point in the pro-fear column.