There were other attempts both recently and not so recently, to come up with a better handgun cartridge, although none of them were created with the military in mind. Perhaps the closest to the .40 S&W Auto would be the .41 Action Express, which I think was introduced about halfway between the 10mm and the .40 S&W (or 10mm short). But the .41 magnum and the .41 Long Colt were other cartridges for similiar purposes.
It is interesting to speculate on the reasons the 9mm Luger became such a world standard. At the time automatics were being introduced for military use, it was only used by the German armed forces and other than the modified Mauser automatics, no other pistols were chambered for it until I suppose the Browning Hi-Power came along. In fact, at the beginning of WWII, it might have been that the Colt .45 automatic was used as much as 9mm pistols, allowing for the fact that the Germans were preparing for the war and we were only just starting to think about it in 1939.
Shoot low, sheriff. They're riding Shetlands!
Underneath the starry flag, civilize 'em with a Krag,
and return us to our own beloved homes!
Buy War Bonds.