How can I really answer this question? Why natural light only? Portraits are portraits, regardless of whether the light is the sun or an electric light, and light is light.
Natural, available light is [usually] different in character. Of course, it is possible for artificial light to approach the qualities of natural light, but even then, one has to wonder if it is even possible to photograph a portrait subject in the same disposition when artificial light is used. People simply feel a lot more comfortable and 'natural' when they don't have big softboxes or flashes or whatever aimed at them.