It's easy to understand if you understand the game most of those pistols are built for.
As has been stated already it's a caliber that was designed for a specific purpose, so it's not a solution looking for a problem; at least it wasn't when it was designed.
I know plenty of people that shoot 38S or it's relative 38 SuperComp and almost all are under 60. The reason they choose this caliber is all about the game. In the Open division of USPSA you are allowed to use ammo that "makes major" (bullet weight*velocity)/1000 >= 165 using a 9mm projectile. You are also allowed as much ammo as you can fit in a 170mm long magazine. If you want the scoring advantage and want to have 30 rounds in the gun then you shoot 38S. As an added benefit you can use a powder that produces a lot of gas which makes the compensator work better and keeps the gun shooting flat even though you're sending a 124gr peojectile downrange at 1450fps.
People are starting to use 9mm loaded to the same velocities more these days but it's not seen as reliable and you have fewer powder choices.
So it started as a solution to a specific problem in the law enforcement world and is now the perfect caliber for USPSA/IPSC. If you like Single Stack 1911s and want more capacity it fits there as well but I don't own anything chambered in it outside of my completion guns