Pocket squares are arguably a different item, with a different, in the case of pocket squares, decorative, not utilitarian, purpose. And pocket squares are generally smaller than handkerchiefs and can be made of materials, such as silk, that one would not likely blow their nose or dry their hands on, or, say mop the seat off his brow with.
That said, a cotton or linen pocket square, at least a plain white one, could serve some of the same purposes, on a one shot basis, as a handkerchief, and would have the benefit of being obviously unused. For instance, I think such a pocket square would be ideal for offering to a woman for purposes of drying her tears. (Not, of course, if one has through intentional behavior caused those tears!)
I think handkerchief were often in the past linen.
That said, a cotton or linen pocket square, at least a plain white one, could serve some of the same purposes, on a one shot basis, as a handkerchief, and would have the benefit of being obviously unused. For instance, I think such a pocket square would be ideal for offering to a woman for purposes of drying her tears. (Not, of course, if one has through intentional behavior caused those tears!)
I think handkerchief were often in the past linen.