The fundamental problem of high-wattage charges (say 500kW), isn't to deliver power from the charger to the car, but that there needs to be crazy amounts of grid capacity to support them. A house has like 10kW peak sustained power consumption (an apt even less), which it rarely reaches, so a park of these fast chargers need the same infrastructure as a small town. These loads are so huge Cities like Beijing have stro…
The first solution is of course to try avoiding farst charging if possible by charging at home or at work over hours if possible. A faster charge will have to be a more expensive charge. Another solution that could ease things a little is to spread the load on the grid over time by drawing it from some local source (e.g. battery) Imagine a gas station has a beefy energy storage from which it draws the current in short blasts while the battery itself draws it much more spread out over hours.
This is essentially how it is done in much smaller scales (in terms of time, energy and actual physical size) on printed circuit boards using capacitors. If you'd draw the current all the way back from the power supply any bursty load would affect the voltage on the power supply and thus show up in other psrts of the circuit.
But in the end more electrical energy demand by mobility will lead to more electrical demand, period. And as you rightly pointed out that means more infrastructure, more copper in the ground, bigger transformers, more powerplants.