Early war 660 & BNZ coded MP-40s were very well made and finished.
We might not much care for the quality of fit and finish on the late war guns, but they were functional for their intended purpose, were safe to shoot, and were made of quality materials. The short cuts were taken only to increase production rates. Why spend a great deal of time on finishing when the combat career of the gun and its bearer would likely be measured in minutes?
The US was the only major combatant that did not adopt this approach, and so never had reason to regret the decision. By regulation, no fitting was allowed during the manufacture of US small arms. All parts were perfectly interchangeable from the beginning of serial production to the end.