Moving the elevator down would only take potential energy out of the system when the elevator together with its load weighs more than the counterweight. When i

Moving the elevator down would only take potential energy out of the system when the elevator together with its load weighs more than the counterweight. When it does, you might be able to use it to generate electricity. But I wouldn't be surprised if that isn't done simply because it wouldn't justify the added cost and complexity of building all that extra energy harvesting mechanism into the elevator.