I think they went out of style for actual use with the advent of more hygienic disposable tissues. Who wants to carry soggy snot bombs around? It's like one step up from a dirty diaper. I guess as a fashion accessory for the snappy dresser a dress hanky is a necessity. Maybe offer it to a lady if she has to dab a tear or something. It's more classy than just tossing her a pack of Kleenex.
Yes, I carry one. In my work environment a kleenex is not always available but I seldom use it for a snot rag. If so, it just goes in the laundry and I grab a fresh one. Dust storms are frequent. Sweaty here in the summer. Nice and cool when it's wet down in a water fountain. Wipe off the lunch table.
You really ned to get a shemagh as an all-purpose cloth.
Fill with pennies and make an impromptu life preserver.
Fill with ice cubes for a cold compress
Use as a white flag and surrender
A miniature Jolly Roger! (black hanky only)
Tie off a bleeding finger
Use as a gag (might also need duct tape)
Cover your canary to make him fall asleep.
Plug a hole in your canoe.
Use as a pall for your dead hamster or goldfish.
Hanky magic tricks for the kids!
They are handy. I sometimes wear one around my neck as a scarf in winter. A bit big to stuff into your pocket in the summer, however.