You may find this AMA of interest as the answer is touched on there. To sum up what I and other panelists note there, the importance of a semi-auto rifle wasn't recognized enough by Germany in the '30s, and by the '40s, they did start making them, but it isn't that simple to just switch production and rearm millions with a whole new gun in the middle of a war. You are, however, mistaken to think that "most other nations adopted semi-auto rifles as their infantry weapon of choice rather quickly". The US of course had before entering the war, but no other major country fully rearmed with a semi-auto by its end, although a few others did partial implementation, and Germany was actually more at the forefront, with over 400,000 deployed, than it was behind the pack.