If everyone drove an eletric car, our eletric bills would be increasing at a very rapid rate, instead of gas prices. Moving the problem from one location to another has never solved a problem.
Sure it has. In this example, its a lot more efficient to make electricity at a huge power station, utilizing economies of scale, than it is to utilize millions of very small and inefficient gasoline and diesel engines. It matters not if the power station is using coal, natural gas, some other oil derived fuel, nuclear, solar, hydroelectric, wind, or what have you, it still holds. The increase in cost of electricity, if it happens at all, would be negligible compared to the savings from not buying gasoline. The inherent advantages electricity has in production and distribution guarantee that.
Another factor is that many of our political rivals or straight up enemies are funded by our oil habit, and finding ways to reduce their leverage on us is a good idea.