Most electric cars will charge at night, which is when power consumption is currently at its lowest. Power stations (and other parts of the power infrastructure) have to be sized to the daytime peak, plus a safety margin to cope with at least the loss of any single element. So until the extra consumption from cars charging overnight grows above the difference between the nighttime low and the daytime peak, not much extra infrastructure is needed.

On the other hand, there will be cars charging at daytime (either at fast chargers, or while the owner is at work); and there are some power stations that can only work during the day. I don't know which of these two factors is bigger.