The argumentation is flawed.
1. Just imagine the required charging infrastructure if all vehicles were suddenly battery powered. Charging electric vehicles requires quite some power. Can the power grid installations sustain that (power lines, Transformer stations...) ? What resources (financial and physical (e.g. Cooper)) are required in order to adapt the infrastructure ? Just an example: A supercharger station which can charge a few cars at "full speed" simultaneously can draw > 1 Megawatt. Furthermore, superchargers are quite complex (and expensive) technology;
2. Batteries are not a suitable large scale energy storage. However, non-dispatchable, fluctuating energy sources such as solar and wind power require huge amounts of storage in order to sustain the power demand.