Your hunch is not entirely correct for a couple of reasons having to do with efficiency. A gasoline engine is about 15% fuel to wheel efficient, not counting the cost of crude in the Middle East to refined gasoline in your tank. Coal plants are quite efficient as is the conversion of electricity to mechanical energy in an electric motor.
The real issue is capital cost because of the battery, lifetime, range, and performance.
You haven't factored in the loss while the electricity passes through power cables from the plant through the grid.
The average coal plant is 28 percent efficient, with the best around 45 percent. I think known battery technology is around 50 percent. I’ve read of a Mazda project on a 30 percent engine. I’d like to know what the efficiency of a Prius is, as it seems to be a much better concept than a plug in. I did a calculation once on how much power it would take to charge batteries in a ‘battery swap’ station. The same could be done for an ooze station. Assume 8 pumps, 75 percent used for 12 hours a day, with 10 minutes a fill up....at 10 kwh per fillup. Each night, the station would have to impart over 4,000 kwh over a 12 hour period....and this is just one ‘filling’ station, to let people get 40 miles, with today’s technology. When thee gas station has to knock down the car wash to make room for the transformer, it starts to look very inefficient to me. There are losses in transmitting and stepping down this kind of power.