The charging cables would have to be enormous, though, to fill (say) to a 400 mile range in less than 3 minutes. The currents and voltages required would be absurdly high. Let's say we have a 180kWh battery/capacitor we want to fill in 3 minutes (0.05 hours). The power coupling would be running to the car at 3.6 megawatts during the charge cycle. With a 11kV coupling you'd need a current of almost 330 amps, so big, thick and heavy conductors. Even if the charger was 99% efficient, you'd need to dissipate 36kW of heat energy during charging (about equivalent to the power output of a small car at wide open throttle).
Having quick charging capacitors/batteries isn't even half the challenge of making an electric car charge rapidly.