The cloths on the broadswords are usually called "flags" in form competition. what I was told by my instructor, is that in form competition, the flags act as a signal by their motions if the sword motion is slightly off, at least for some moves. Some schools use them some don't. Usually it is up to the students discretion as to keep them or not, if you find they are really in the way, take them off, I personally like having them for some forms; and don't like them for others. Keep an eye on other students who do forms with flags on their swords, it really is easier to pick up the subtleties of the blades movements. This is the same reason you often see cotton tassles on tai chi swords.