Yes, but it is NOT more efficient than generating all that power, transmitting it, and then putting it into a battery, and reconverting it into mechanical energ

Yes, but it is NOT more efficient than generating all that power, transmitting it, and then putting it into a battery, and reconverting it into mechanical energy again. End-to-end it is LESS efficient. A tank of gas does not lose energy in transmission nor in storage, and it is far far more weight:performance efficient.