That's not completely accurate. The limiting factor is the resistive heating of the cable, relative to the cable's ability to shed that heat. If heat can't leave the cable faster than it is being added, it will eventually melt or burn through the insulation.

If you wrap the cable strands around a cooling tube, you can use water, oil, or a refrigerant to carry away the heat and push a lot more power through a similar sized cable.

Large underground transmission lines have used such methods.

It may be that the charging station will need to actively cool its cables , and the vehicle's air conditioning system might need a second evaporator coil to actively cool the battery and charging circuitry. But it's certainly possible to deliver that amount of power in that short a time frame, without having to resort to "THICCC" cables.