>>3592696because it it shoots bullets reliably enough
If your existing industrial capacity cannot sustain high enough production even prior to massive attrition rates and strategic bombing, the use of captured material to supplement losses and war expedient designs to increase industrial output either through existing manufacturers or by small shops who can manufacture simpler things, or just even just individual parts is necessary..
That and the SS was outside of army arms procurement so they used a lot of arms produced from captured nations facilities (like the ZK-383), production from smaller German firms or captured equipment.
In general
Captured STEN's were fielded
Virtually exact copies down to the British markings for clandestine purposes late war.
Even further simplified versions of the STEN that reduced production time further, and also changed the magazine well to a vertical one MP40 style and also using MP40 magazines.
The latter were more Volksturm, though Skorzeny wanted them to be produced for the SS.