It doesn't 'need' to be running, but that's when there's the most power available to the electrical system, which is what the others were saying, and that's the same with any car so the difference is likely the old and heavy motors vs the newer designs, probably relays etc, and a good battery. If there's a major difference in the speed when car is off then it simply comes down to the battery. Either way it will likely be a lot slower than newer wiper motors even when good, but a 50% reduction sounds like a lot. Without the motor connected you can also operate the wipes back and forth to make sure there's no binding in the linkages, clean the ball pivot out too but mark where it is as it can be adjusted too.