Exactly true when you are charging up tens of thousands of vehicles, especially as you pointed out, when people get home at 6:00 PM, immediately recharge their vehicle, while preparing meals .
That would be a significant power draw between the hours of 5 PM through 7:30 PM ;
I'm not sure the grid could handle the evening surge with all the home appliances operating at the same time.
The only realistic alternative would be to have separate electric meters for home appliance usage, and recharging stations on a timer to charge up during 'off peak' hours.
Even if you say had EVs begin charging at 9:30 once the peak evening load of cooking, clothes washing, etc. has passed you are just gonna create a new peak load later. These hours of the day this is usually little winds and no sun, so all these EVs will be charged with eeeeevil coal, natural gas or nuclear. Hahaha.