"From my point of view the only thing that stops us all from switching to electric cars is the battery technology."
My obvious point was that, in fact, that is not even remotely the only thing stopping us from switching to electric cars. My scenario was extremely useful in highlighting the fact that we do not have the capacity to switch to an all-electric car approach, and not primarily due to batteries.
We can do the battery tech and manufacturing in the present, to build very effective electric vehicles. Building up the grid to support ~500 million cars in the first world would cost tens of trillions of dollars and take decades. It makes the battery challenge look hilariously minuscule by comparison.