Not sure why the short action .308 came about
It was developed as a military cartridge (7.62x51mm NATO) to replace the .30-06 for use in belt fed machineguns with disintigrating link type belts. The shorter cartridge meant a shorter bolt travel, higher rates of fire, more compact, lighter weight ammo and easier to handle belts that aren't as prone to twisting and jamming. The military wanted a short action .308cal cartridge that would closely match the performance of the standard 150gr ball .30-06 loads, and the 7.62x51 NATO does that nicely. The .308 Winchester is the "domesticated" version of the military cartridge.
Mike