Did you just invent an EV supercharger?
Seriously, though, to generate the ~190kW that the Roadster uses, you'd need over 6000 kg of batteries! You would, presumably, use some kind of power buffer (like an ultracap) to cover for bursts, but you'd still need the main battery to provide the long-haul average power. At 250Wh/mile and 60 m/h, you need 15kW sustained, which would still be 500kg of batteries at 30 W/kg. That's somewhat bigger than the Roadster's battery, and still kind of on the weak side.
That is, I think to be useful in cars, they need a big improvement in power density.