we essentially do the same thing but slightly different with hybrid cars like the prius. the difference is that the engine doesn't JUST generate electricity.

the problem I see with your idea is that generally it would be far more efficient to just use the "portable power" to power the car. of course, with a theoretical "free energy" device that wouldn't be an issue, but such a device does not and almost certainly will not exist, and especially not on a scale large enough to power every single car in the world.