The idea that this was an American response to earlier British innovations is a good explanation. The rim construction and styling was drawn from British innovations that occurred before and immediately after WWII. By 1948, the tubular/double-layer style rims were common for the Endrick and Westrick types. Unfortunately, the British catalogs do not seem to have made as big a deal about the rim construction as they did about the move toward chrome plating and stainless spokes in the 1930s. The pre-war catalogs tend to simply say that a better-quality bike has "Endrick" rims with chrome plating and stainless spokes. The 1948 Raleigh spares catalog does show the double-layer style construction for several patterns of rim.
Generally, American lightweight design in the 1930s-40s was reactive to British introductions and innovations. The pre-war Schwinn lightweight appears in its style and design to be based on pre-war Hercules (frame, equipment, some of the threading and sizing) and BSA (the three-piece crank chainrings on the New Worlds, for example), though with Schwinn adaptations to the construction and equipment. Schwinn touted its lightweights in the couple years immediately before Pearl Harbor, whereas similar cable brake multi-speed bikes had been available in Britain for quite a few years by that time.
Schwinn's move to the 597mm rim rather conveniently also matches the fact that the same rim size was used by the "sportier" British bikes running 26 x 1-1/4 tires. Unfortunately, Schwinn stuck to 597mm for its lightweights, cursing us with only Kenda tires 70 years later (going to the British 590mm would have been nice for us today). The Kendas aren't bad, but I'd love to be able to get a good set of Michelins for my Schwinns like I have on some of my Raleighs.
The other thing to consider is that when Raleigh came on strong in the US after 1945, their products represented an upgrade over the more basic pre-war Hercules bikes that were sometimes seen in the US. The competition was definitely stronger after 1945, and the vast majority of "foreign" type bikes in the US were British in that period.
I don't think Schwinn invented the basic tubular/double-wall rim concept, but it seems to me their focus was on improving it as to joinery, production ability, and plating.
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