Would we be able to insulate sufficiently for a new generation of DC fast charging where voltage is so much higher that current is so much lower that the cable isn't thick enough to be worth stealing? Could eliminate active cable cooling, as well.

I guess the problem would be stepping it back down inside the car to match the battery voltage, which is an AC endeavor, at which point it might as well just be AC grid power delivered to the car (albeit high/primary voltage, not residential/secondary voltage), and we're back to the car having enormous equipment on board that ought to be stationed, so no.