Power companies can manage load. The power provider I'm with manages my charging. All I have to do is pick a time when I want it to be ready (the power company not only gives the half rate night pricing, it also pays me to do this). There's a lot of excess energy at night, off-peak. Millions of vehicles smart charging will balance the load.

The issue is, when millions want/need to charge at peak. Which, I haven't really seen yet (having owned an EV for 4 years now). Mainly because, it's more expensive to do so. What I have seen is the grid being overloaded because of students doing all the heating, laundry, dishwashing and showering when power companies offer a "free hour of power" and they all choose the same hour according to student scheduling (they prefer timeslots between 1600 to 2200)... But I haven't seen the grid go down because of EV's, we mainly pick the later timeslots (2300 to 0700).