Most people get off work between 4 and 6pm. (this is not 50% of the population, but it is still a large number). They all go home and plug their car in then take a shower. Many days the peak electric use for the day is at 6pm when all those people start cooking dinner (electric stove) or jump in the shower (electric water heater). When a significant number of people start plugging their car in when they get home the peak will go up much more.

Of course as has been pointed out repeatedly a smart charger can manage exactly when the battery starts to charge. However it isn't quite that simple: many of those people will go out again for their bowling league or whatever, and need enough charge in their car.