problem is real but pretty easily solvable
Yes, a lot of people will get home at 6pm and plug in their EVs for the night. Yes, if those chargers start pumping as much energy as possible into the EV battery packs during the evening peak, the distribution networks are going to be seriously tested.
But who said that all these future EVs need dumb charging? The chargers themselves could have a 3G connection that negotiated charging times and rates with the grid operator in exchange for a small discounted rate during those times. You could have a website where you could for a nominal fee reserve immediate charging time slots if there was a reason you needed a quick top up at volume 11. Better still, auction off those slots to the highest bidder and earmark all profits t from those auctions to distribution network improvements. Finally, incentivise EV owners to let the grid take back a certain number of KWhr over a particular portions of time for grid stability services. For example, let's use some numbers. Assume a 50KWhr battery pack. If you could be paid by the grid for giving back the top 5KWhr (so your available capacity was guaranteed to be at least 45KWhr). They could for example credit 10KWHr free electricity for those 5 you gave back when the grid was struggling.