I just thought of something. Perhaps there is some truth to this theory.
The last group of BMT standards which were retired in 1969 (200+ cars) were rebuilt in the late 50s. I don't know any specific details of what was done, but I get the feeling that the door controls may have been relocated to the motorman's cabs on those particular cars.
When I rode the standards on the Canarsie line from 1967 to 1969, I would sit in the middle of the train, usually the third or fourth car of a typical 6-car train, on the trip from 8th Ave. to Lorimer St. I know for a fact that I never saw the conductor at any of the center doors, although I remember the control buttons. I do remember seeing the conductor in one of the cabs after getting off at Lorimer. On the way back to Manhattan, I always stood in the first car, 2x4 or no 2x4. After the R-1/9s and R-42s arrived, I stood in the first car on the way to Brooklyn as well. BTW, I'll bet that if a storm door could not be kept closed and locked today, they would probably evacuate the car and isolate it from the rest of the train; i. e., the doors of that car would not open at stations. I saw them do that once on a train of R-44s after the window of the door to the motorman's cab fell out when someone leaned against it.
Getting back to the standards, the dragging issue raises a good question: how did conductors check for anyone being dragged if they were standing by the center doors? Passenger entry doors did not have opening windows, although the storm doors on the standards did. Back in the days when each car had a conductor, it would have been easier to spot someone being dragged.