Another earlier example following pretty much the same approach is the genesis of the German 'Schmeisser', though the MP40 (and its final iteration the MP41 - which basically had a wooden stock) was actually designed by someone else (Heinrich Vollmer). Schmeisser designed the much earlier MP18.
Anyway - my point is that at the time the allies were touting the more-or-less unchanged 1921 and 1928 designed Thompson, Germany was knocking out well over a million MP40s between 1940 and 1945 because of its inherent simpler design. Whereas the Thompson was largely composed of machined metal requiring a more involved (and slower) manufacturing process, the MP40 was knocked out mostly from pressed steel and welded parts. Even the 'cladding' on the grip areas was 'bakelite' over metal with a folding frame stock, rather than the more involved staged fabrication of wooden grip and stock.
We wake up to this whole approach with the Sten, and the USA doesn't find a similar mass-production solution until the advent of the M3 - or 'Grease Gun' introduced 1942'ish?. And if I remember correctly, the Sten only rushes into production from 1940/41 because of the acute weapon shortage following on from Dunkirk, and the fact we couldn't get enough Thompsons from the US. Mind you, we then proceed to churn out over 4 million of them up to the end of the war and beyond.
Needless to say - the greatest exponent of this whole 'genre' is - of course - the AK/Kalashnikov.
Depressing ... isn't it! Our ability to simplify and 'improve' the art of war.
Richard