This isn't quite as impractical as you assume. I don't foresee an all electric car scenario anytime soon, but the total energy use in the transportation sector is only a little over half of the current electrical energy use. By increasing the number of power plants by 50% we could at least switch all passenger cars to electric. There is a potential silver lining in this also as most charging could probably done off-peak, at night, allowing more of the power plants to be base load and minimizing the stress on the electric grid (distribution system).
The efficiency impact of electric cars is pretty complex. Gasoline engines are limited to thermal efficiencies in the 30 to 35% range, as I recall and there is no mechanism for regeneration (capturing braking energy). On the other hand, electric motors can easily be 95% efficient and allow regeneration. On the electric generation side, coal plants typically have over 40% thermal efficiency and combined cycle gas plants can exceed 60% thermal efficiency. Losses in transmission are generally less than 10%. I don't know what the charge/discharge efficiency of the advanced batteries would be now. If the electricity is generated by wind, solar, nuclear or hydro, the efficiency probably isn't something to be considered, only cost.
The modern internal combustion engine is a marvel, but there are efficiency limitations in the Otto cycle (and it's offshoots) that will keep it's efficiency well below a central station power plant.