Back on topic
I think it was a a matter of focus and money, and attitude.
The English had no money (sound familiar) after all there would not be another war. They cut back on all most all military development for a number of years prior to the start of war.
The Germans focused on the aircraft, tanks and squad MG's the MG 34 was functionally the 1st GPMG in service. The general idea was the rifleman supported the MG's not the other way around. The production capacity was spent on those items.
In the US case, there were some individuals who at, least in the area of the basic infantry rifle saw the need for a better system and got it built. But even then look at the initial production numbers they were quite low until the US got into the war, when they ramped right up
As to focus the European countries all derived different lessons from WW1 than the US. Heavy losses and generally bad leadership, lead most to believe the artillery, machine guns and slow moving armour were the way to go. The basic infantry would be supported by those weapons, so his basic kit was perfectly fine.
The US having less time in the trenches, seems to have drawn the conclusion that a smaller round that could be fired faster would be a better solution. But SMG type solutions were not acceptable.
The Germans went more to SMG's, based on the stormtrooper tactics of World War 1, where quick firing light automatic weapons were preferred. Once again leaving the basic rifleman with his bolt action rifle.