If there were a big swing toward electric vehicles, I could see that infrastructure having a hard time keeping up.
I charge my Smart Electric Drive overnight on 12A 120V and am good to go on or before 6am if needed. If millions of Ontarians drove electric cars, this would finally make use of the excess electricity we are currently selling at a loss during the middle of the night when Ontario has "surplus base load" generation from Nuclear and Hydro.
My commute is 30km a day, which in the winter is 8KWh of electricity, and in the summer, more like 4KWh for the same commute (as I don't need to run defrost, heater and heated seats). I use the L1 EVSE that came with the car, and recharge at a rate of 1.5KW.
If 1 million cars were recharging simultaneously using 1.5KW, this load would be less than the peak air conditioning load in the summer, and again, the load would be in the middle of the night, when electricity use is historically the lowest.