Have to throw my two cents worth in ... My personal belief is that the open fan idea came about due to kenbu, traditional Japanese sword dancing. I know there are a couple of Japanese sword arts lines that still perform kenbu. I also know that there are a number of kenbu that utilize an open fan. It seems to me that at some point, people saw a kenbu performance and mistook it for kata, then went on to incorporate this "traditional Japanese fan art " into their practice.
Here's an interesting article on traditional kenbu at EJMAS ... The Fan and the Sword
Here's an interesting article on traditional kenbu at EJMAS ... The Fan and the Sword