Eh... not really. Doing that is actually not very efficient because of all the losses you incur going from AC to DC, into the battery, then out of the battery,

Eh... not really. Doing that is actually not very efficient because of all the losses you incur going from AC to DC, into the battery, then out of the battery, back to AC and into the motor. The Honda Accord Hybrid, Mitsubishi Outlander and BMW I3 do something like what you describe, but they take the energy straight out of the generator, which still has some losses, but is made up for by the lack of a multi-speed transmission. None of those cars will charge the battery past a bare minimum at stop lights.