There are a lot of legends about bands. Gustave Bock has been credited with the popularization of paper bands to identify the cigar makers in the mid 1800s. From all I've read, bands were added simply for branding.
The legend about cigar staining the white gloves of "Fancy Dans" or "Jim Dandies" comes from the late 1700s when cigars were finished with a chicory-shaded gum and rolled in a fine tobacco powder (pulverized dried leaf). This finishing process was necessary because the wrapper leaf [back then] was crude and uneven in color and finish. The powder finish provided a desirable even color but quite possibly stained the fingers or, in the case of "Jim Dandies" . . . their white gloves.
Brit's and some European cultures encourage the removal of bands as proper etiquette. However, I've been told that they remove the band and place the band on the table in front of them, thus showing what brand they are smoking! Doesn't that kind of contradict the idea of removing it for snob factor?
I take bands off when possible with no damage to the wrapper. . . usually when the burn gets close to the band which heats the glue and makes it easier to remove.
I also save bands. . . but, haven't much interest in collages. However, I would like to make a poster size
Photo Mosaic using the various bands as the color pixels. Just waiting to find the right photo.