The batteries are the same size that they were previously, so the kWh pulled from the grid doesn't change.
Industrial users with electric arc furnaces and other massive loads need special, ongoing arrangements with the utility to operate safely on the grid. It would only take 200~300 of these high speed chargers to equate to the demand of the largest EAFs on earth.
This theoretical car draws 1 MW for 5 minutes, pulling 83 kWh. Your normal residential address in America only uses 20 kWh all day long. The hard limit in a lot of areas is 25-30 kW continuous. Sure, they're building special charging stations, yet this is like 40 residential addresses running at max line limit consumption suddenly.
Looking at this a different way, lighting the entire SoFi Stadium (3.5 Disneylands for another scale), takes 10 MW. [1][2] Ten (10) of these cars pulling on the grid is like lighting an entire NFL scale stadium on game day.
[1] https://brilliantsourceenergy.com/the-power-of-the-super-bow...
[2] https://time.com/3926325/nfl-super-bowl-energy-usage/
Looking at something like Electricity Maps [3], the entire state of Texas is producing 47,700 MW (11.6 GW Gas, 24.3 GW Wind, 6.7 GW Coal, 5 GW Nuclear, and they're only exchanging 25 MW across their borders with other utilities. 25 of these cars is Texas's border electricity exchange.
Enormous, multi-state electricity organizations. Have 1000 of these show up to gas stations in some place like Texas, and you're suddenly pulling a substation chunk of the entire Texas electric grid all at once.
[3] https://app.electricitymaps.com/zone/US-TEX-ERCO/72h/hourly