I don't think Patton went through Basic, and when he arrived for "Beast Barracks" or whatever they call it at West Point (he graduated in 1909 IIRC) ,the official Army rifle was the M1903, the cadets used Krags for D&C.
Why didn't the Germans develop and adopt a semi-auto rifle? They didn't see the need for one. Speer blames Hitler for being the WWI infantryman clinging to his familiar "carbine". Again, took John Garand about 16 years-1916-1932-to develop the M-1 then another 4 years of work after MacArthur disapproved of the .270 round. Each nation's armament is a result of tactical
doctrines, its industrial base and educational establishment, the whims of its Ruler, its battle experience, etc.