Is it possible that the witches hat is an exaggeration of the tall conical “Dunces Hat”, popular in the royal courts during the 15th century? or the blunt-topped hats worn by the Puritans and Welsh of the same period? At one point long ago, pointed hats were a fashion icon in the city of London (then the fashion capital of Europe), but it took a long time for fashion to trickle into the country, and by the time they did, they became way out of fashion in the city. City folk called Country folk 'pagani' (which means country dweller), much the same as calling someone ‘a hick’, today.
Pointed hats soon became considered something only the 'pagani' would wear, most were Herbalists and Farmers wife’s who lived in the country and understood the land. Since they were wise to the ways of nature and could grow and harvest herbs, so the pointed hat became associated with the ‘Wise Woman’ or ‘Witch'. During this same period the Christian Church chipped-in and associated pointed hats with the horns of the Devil, by which time they frowned upon their use.
Today, some witches used the point hat as a tool for directing energy. The energy of the universe is drawn into the point of the hat and brought downward to the third eye for manifesting one's intention. From the third eye the energy of the intention is then sent outward into the brim of the hat and out into the universe in every direction, to be manifested.