Maybe. It depends on exactly where. He cites simultaneous draw from many commuters at once. If the utilities incentivized slower charging overnight through pricing (which is something that they already do for power intensive industries) then this would be greatly ameliorated. Also, in many places, as noted by the op, people will start charging after getting home from work. If charging is delayed by just 3 hours, they will merely be using capacity that already exists for running air conditioners.
Problem 2: Rapid charging is actually not so rapid, highway re-charging stations will have to be much larger than current gas stations
Op is assuming the same structure as gas stations. No need for this. What if the car companies implemented a "charge crawl" feature, where a charging car would slowly inch down a track for a half hour while charging, attached to an overhead suspended cable? Actually, there's no need for that. Just have lots of parking, with each space with a charger. Most road trip rest stops take about 1/2 hour anyhow -- and that's when I'm in drill-sergeant mode with my passengers.
Problem 3: Gas stations are not generally in the neighbourhood of electricity generation stations.
Tesla is already building stations that get power from solar.
Problem 4: Re-charging will not work nearly as well when vehicle utilization goes up due to sharing
Consumers may not want battery swaps yet, but car-share companies might well want it.