Ben, I would never put one on my head. Mostly because my head is too big for a bandana to fit. Besides, I really like my Tilley.
But I won't leave for the trail without one either. There are so many uses for a bandana -- towel, water filter, neck shade, bandage, compression in first aid, hot pan holder, lens cloth, place mat, wash cloth, dust mask, cold compress, glasses case, etc.