"AND they beef up the national grid to handle the added load required to charge them..... Probably not in my granddaughter's lifetime."
Of course it will. You are overestimating the requirements of the grid. Firstly the amount of electricity to produce petroleum is quite high, varying figures are mentioned but it is between 50 and 90% of that required to run an electric car in the same distance.
Then you have the fact that many electric cars can charge overnight when little electricity is in use (cheap night tariffs, timer switches or smart electrical networks).
Then small gas powered, nuclear or even large scale renewables could cover the rest.
So you have the power sources sorted, the actual infrastructure can gradually be upgraded as required. It isn't that difficult to upgraded a substation or increase the UHV cable capacity. As long as it is gradual and not required in 5 years time. It's only a bit more difficult than getting FTTH for everyone.
However with vehicles able to do 300 miles per charge and the average (UK) mileage of 7,900 miles p/a this would mean that a car would only need to charge on average twice a month. So the simultaneous charging will be spread out. Many cars will also be charged at service stations as well, with high speed charging and dedicated substations and electric supplies.
I'm pretty confident that there will not be an electricity problem (in the UK at least ) with the gradual introduction of EVs up to 2040 (when no more petrol/diesel can be sold).