3/8" drive certainly existed then, and it's listed in Plomb catalogs of the day, but that film was intended for military training, and most of their stuff was BIG, or really
small.
Even in the civilian market, cars and trucks had lots of space under the hood, and you rarely needed to be a contortionist or magician to reach things. 1/2" drive sockets fit just about everywhere, and if not, you used a box or open-end wrench.
There were also no fine-toothed ratchets because there wasn't a screaming need for them. A plain coarse-toothed ratchet and 12-point sockets could get you operating clearance in most situations.
I'm sure you already know this, but the older Plomb catalogs called 1/4" drive "midget" and 3/8" drive "cub" and 1/2" drive "standard." I don't think they stopped calling 1/2" drive "standard" until the Ingersoll-Rand era in the '60s.
FWIW, my first socket set in the late 1950s, given to me by my dad, was 1/2" drive (new Snap-On sockets and a spare Plomb ratchet of his). It worked fine on a '51 Buick and a '55 Chevy. I've still got the ratchet and most of the sockets (damn kids), and wish I still had the '55 Chevy.