So it's like this, when the motor is at 0 rpm, and you feed the coil voltage, there is the inductance of the coil (which is quickly "overcome") and the resistance. So the maximum torque of the motor is related to whatever the maximum amperage the coils can handle. As it gets moving along the rotor is rotating in the same direction as the current (in some sense) and creates a back emf so the max current drops.
A superconductor removes the motor's power limitation, but telling a battery to supply that energy is, precisely as you say, going to drain the battery too fast. Not only that, batteries have a maximum current supply issue that cannot be overcome without adding more batteries. Batteries have crap energy density (which theoretically can increase a few times, but we won't be seeing that for a while), and afaik the issue of degradation still has not been tackled. A gasoline motor can have very high specific output and very reasonable efficiency, but being tied to a finite number of gears definitely hurts its prospects. In order to create an excess of torque for a significant speed range like the tesla has, you need quite a bit of displacement/etc., and keeping that kind of engine fuel efficient and reasonable for daily use is much more difficult. Given that the Tesla's motor weighs a ridiculously low 70 pounds or something, I think a fully electric drivetrain coupled to a high rev motor can have similar weight and give you a faster car in the end (with much much better fuel economy).
The main thing standing in the way is the size of the generator; if we gear it so that the engine spins at 1/3 the speed of the generator, so we can use a smaller one, there are more losses. So this is just a pipe dream waiting on stuff in the future
