The already existing 1 MW chargers have internal batteries, so they do not need from the grid the peak power, but only the average power.

The average power is lower, as there are idle times between cars. Moreover, in the beginning only a few cars would be able to charge at 1 MW, so the average power will be even lower, allowing a later upgrade of the connection to the electrical grid, when fast-charging cars would become more frequent and when there would also be more EV owners, so that more cars would have to be charged per day.