Fuel pumps that don't run when powered are obviously bad! BUT! Like al mechanical things failure comes in many ways.
The fuel pump does not control the pressure but is designed to work at a pressure range. If the fuel delivery were to become pluged the pump would hurt itself if the pressures possible were allowed to happen (fuel is not compressable).
There is an internal check valve that by-passes when (or if) this ever happened. Its pressure is relatively close to the working pressure (higher by maybe 25%). If this valve leaks, sticks or is broken the fuel just gets pumped in circles.
There are many ways that the fuel pump can become the fuel pressure regulator. When this happens fuel control becomes impossible. All K type systems require precise, constant fuel pressure to funtion properly (or at all).
Bosch Master, ASE Master, L1
33 years MB technician