I read such a quote several times in this thread, and this is BS.
If we switch to EVs this would add between 10% (UK) and 15% (Germany) to the electricity demand.
For 1 million cars it would add ~0,35% and for 45 million cars ~15% in Germany.
In the same time the overall demand is also rising based on growth of population. There is always the need for more electricity, and EVs are just a part of it.
It is not BS, but misunderstanding. Problem is not increased average consumption in kW/h.
Problem is in maximum installed peak power of distribution network.
In Croatia, average household distribution connection is specified for 6 kVA of continuous power. If you need more, no problem, but you have to pay additionally for privilege of being able to pull more peak power on demand. You pay that in addition to all the kW/h you spend.
Rationale behind it is that 10 households time 6 kVA in a street can be served with a small inexpensive 60kVA transformer. If all of them want to charge a car at night , and need 20 kVA of power for 8 hours, you need much larger 200kVA transformer in local substation. And then every larger transformers feeding those small ones has to be upgraded to larger capacity. And on and on.
In Croatia, if every household would have one EV, peak power of national grid would have to be substantially upgraded (80-100 %), although average electricity consumption would go up 20-25%.
All of that is far from show stopper, and would be solved with technologically quite traditional upgrade...
But that has to be said, and it is something that has to be done before EV can be mainstream.....