Originally Posted by T. A. Gardner

The US M-3 'grease gun' was introduced because of the cost and time involved in manufacturing the Thompson. General Motors engineered the M-3 along the same thinking as the PPSH: Cheap and reliable. Another interesting feature was its deliberate design included the ability to change the ammunition by replacing the barrel and receiver so .45 or 9mm could be used although this was rarely used in service.
As for cost the M-3 was $11 to manufacture versus $25 for a Thompson.

An interesting in service practice late war by GIs was for infantry units operating with tanks in more urban areas to swap their M-1 rifles for the tanker's M-3's for house fighting and the swap back when finished. This could result in a US infantry company having hundreds of submachineguns in use during an urban fight. It wasn't doctrine, but it did happen.