The reality of the situation is that most people who buy an EV will use fast charging only a few times a year. The majority will be charging overnight to recuperate their daily use, which amounts to drawing <1% of a MW. The grid, in it's current form, is totally capable of this.
What would be a strain though is large ultra fast charging stations along major travel corridors. But I'd still wager that those will be overkill for most.