We would not last long without it. But it is not an appropriate response to a threat to an artificial psychological self. In this role, fear is compromising, not aiding our survival, and in several different ways. Fear can lead to stress, and thence to various physical, mental and emotional ailments. Fear that our sense of identity may be damaged leads us to judge the people we interact with, and live with.
Fear also leads to worry.
But while our attention is caught up in the past or the future it is not in the present moment. Perhaps the saddest irony of all is that this worry prevents us from finding that which we are really seeking. At root we all want to feel good inside. Quite naturally, we want to avoid pain and suffering, and feel more at peace. But a mind that is busy worrying cannot be at peace.