It looks like the New York subway conductor is positioned in the center of the train so that they can check to make sure everyone is clear better. They also show them looking out as the train starts moving to make sure everything is still clear. The BART operator says the train starts automatically. He does his check then goes back to looking forward as the train starts to move. Someone waving frantically would not be seen.

I work in engineering designing tools that work automatically. An obvious big concern is safety - how to put it in safe mode if something unforeseen happens. It's hard to identify all the risks. I assume that BART has safety interlock switches that trip preventing train movement if the doors are not fully closed. Obviously they would work if a persons body, hand or foot was in the way. But as others have said, the leash was not thick enough to hold the door apart so that the safety's tripped. That makes sense. If the doors close tight enough to sense a leash in it then they would create a pinch hazard. The doors are designed to have a clearance between them with a compliant rubber gasket that makes the seal for that reason - its safer.