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Electric vehicles would reduce energy cost as they are about 3 times as efficient as gas vehicles, which expel most of their energy in heat not forward motion.
In my original analysis I made the mistake to think Elon was talking about 100 square miles not 100x100 miles (10,000 square miles). While he's still overly optimistic, by about 50%, at least he's in the ballpark.
It's still very impractical, imagine what something like that would cost to maintain? One worker per football field size array of solar panels would equate to about 10 million workers. I guess with robotics this may become feasible, but not for a while.
You are missing the point that a change to entirely electric cars will require much more electrical power than is currently being used.