The carbine was the only WWII firearm I can think of that used a short stroke piston, but that is irrelevant to its tactical role which was, as noted, to replace the pistol.
Before WWII, the Army TO&E called for a large number of troops to carry pistols. That included company commanders, platoon leaders and assistant platoon leaders, squad leaders and assistant squad leaders, machinegunners and assistant gunners, BAR men and assistants, mortar crews, photographers (not signal personnel generally), military police, etc. (In spite of the catch phrase, "cooks and bakers" usually had rifles, and so did the airborne. Tankers never had carbines, always pistols or SMG's and never "Tanker Garands" either - those were faked rifles given a fake name.)
Given the experience in WWI, the Army was concerned in two areas. One was that in a larger mobilization there would again be a shortage of pistols, as there had been in WWI. The other concern was that in that way, those issued pistols proved to be not quite the "dead eye dicks" of legend. Those hardy descendants of Old West gunfighters simply couldn't shoot a pistol!
Hence the carbine. Light enough to be less of a burden to troops whose main duty was not shooting at the enemy, yet accurate and powerful enough to be effective when needed.
Jim