The reason the M-3 grease gun lived so long, was that it fit very nicely inside a tank. Its role was that of a ‘crew served weapon’ for when one of the crew dismounted the tank. The M-1, M-14, and M-16 were too long to find a safe storage location inside of a cramped tank compartment. I remember one of our 2LT Forward Observers taking his M-16 inside the tank he used to FO from, after being told NOT to by the CO, and the M-16 ending up as a pretzel.
Other posters have mentioned the slow cyclic rate of the grease gun as a deficiency for being a SMG and I agree. I had a friend who was a LRRP in Vietnam and he swore by the Swedish K SMG he carried on patrols.
I have no comment on which of the new SMGs should be adopted but the Grease Gun’s day is passed as a general issue SMG.
The Turret Monster has eaten a lot of M-16s.