I can only guess that with the prevalence of mobile chess apps, individuals lost the need to carry such a set around. However, there is still a company that produces pocket chess sets inspired by such vintage designs.
chessmate.com
There pocket chess sets are magnetic and have a magnetic base to put all captured pieces. I have ordered one myself and am awaiting its arrival.
If you ever search online about pocket sets you will usually see an older version of pocket sets leather or something, but now people use a newer version, magnetic. The ones on amazon if you search it, the thing with those is that after you take a piece there will not be a place to put it. But the older ones, there is usually a slot to put it, to me those older ones are more easier to carry around without fallen pieces. Does anyone know why they don't produce those anymore?