Possibly even more significant, those are some large cables and even larger contacts required. There's no way a 1MW disconnect is just a little plug you stick into your car.

In fact as an electrician I can't think of anything even near megawatt class that would be connected with a portable cord, or at a voltage that would be safe for consumers to handle.

Maybe someone in the mining industry or similar can chime in, but I currently run a pumping station that includes 3000HP motors (2.2MW). These are 4kV 3 phase units where each phase cable is as thick as your arm. All connections are bolted and taped to avoid corona discharge. Just dragging the cable to the car would be more than the average driver could handle.

I don't see a way to get these power levels into a car short of a standardized and semi-automated docking system. Or maybe go back to the idea of standard swappable batteries where the battery then is charged rapidly for the next customer.