Ummmm... I think we have to be sure to differentiate between the M1 Carbine and the earlier (1928) M1 Garand... I rarely disagree with the venerable heathfield but the M1 Carbine (1941) was manufactured in the .30 caliber (similar to the Britsh .303) while the Garand, being considered an actual assault rifle was produced in the more powerful 30-06 caliber. The Garand had been around quite a bit longer but a light weight, easily carried weapon was needed so the M1 carbine was produced in record time. Actually, the Germans as well as the Brits had produced semi-automatic weapons from earlier designs (The very first automatic rifle was invented by James Puckle in 1718... an Englishman... similar to later Gatling Gun)
I suspect heathfield is correct though, in stating, especially in the inter-WW period following the devastation and bankruptcy that followed WWI, that inovations in automatic weaponry followed the available calibers with little incentive, until outbreak of hostilities, to make such advances, as is mostly true of all such historical changes, in my opinion...