My father carried one of these in his pocket every single day, never leaving the house without it. He used it to wipe the sweat off his brow and once, as a tourniquet tied around my finger when I was a child to dig out a nasty splinter with his pocket knife.
My grandfather had a collection and while a lot of things find their way back (straight razors, vinyl records, fountain pens, boxers, ANTIFA…) I think the handkerchief died along with suspenders and hats.