I’ve carried handkerchiefs for a long time, but I normally carry a pocket pack of Kleenex to use for blowing my nose. I most often use my cotton hanky to clean my glasses, but I have used it as part of my duties as an uncle to clean wounds, dry tears, and blue noses.
A wise man told me long ago that every gentleman has a cotton handkerchief, a lighter, and a knife in his pocket at all times, so unless I’m going into a place where the knife and/or lighter are prohibited, I always have those items in my pocket.