###carbon in motion
Even if the extra electricity is provided by coal, an electric vehicle is so much more efficient than a fossil car, that there will be carbon savings: electric cars are typically 80-90% efficient, compared to about 20% for a fossil car. So even with a coal plant at 33% efficiency, there'there's still a carbon saving from the electric.
Electric cars are about 4x4× as efficient as fossil-fuelled combustion engines, tank-to-wheel: ICE engine efficiency is around 20%. Electric engines tend to be around 80-90%. For the whole-cycle energy-efficiency, then well-to-wheel would be the efficiency you were after, and then it would be very sensitive to how your electricity would be generated.
For more information on efficiencies power"power-station to wheelwheel" efficiencies of electric vehicles, see the US Gov Fuel Economy site.
So in general, yes, electric cars are a significant improvement over their fossil-fuel guzzling competitors. I've seen no evidence that the batteries end up at ain landfill after just 3 years of life - that seems to be a bizarre and unsupported claim. SuchSuch a practice would not be remotely sustainable. I have seen evidence that some manufactures are seeking to recover the batteries: presently, at least here in the UK, a lot of electric-car suppliers are leasing, rather than selling, the batteries, which means that they'll go back to the manufacturer at the end of their life for complete recycling. After all, a dead battery contains all the ingredients needed to make a brand-new battery - the thing that needs doing, is reversing all the decay chemistry, which is just a question of energy inputs.
Patterns both of car ownership and use have changed hugely in the last 4 decades. And the change in the 4 decades before that was huge too. 4 decades is enough for really big changes in transport patterns. For several reasons. It's 1.5-2 generations, giving plenty of time for cultural attitudes to shift. It'sIt's long enough for disruptive technological innovations to gain big market share. And it's long enough for a sufficient amount of land-use to be reshaped around new transport patterns.