In normal driving you accelerate to highway speeds and then coast, or you're in city traffic and benefit from regenerative braking.
On a track, you brake late on purpose because it's faster, but to stop that fast you have to rely more on traditional braking and can't recover the energy. Then you immediately want to accelerate back to high speeds again.
If you put a small battery in an electric track car, it would be flat in ten minutes.
Next year they’re supposed to increase power output to 350kW, which is comparable to a Model 3 Performance. Of course Formula E cars are much lighter, so acceleration and handling are far better than the Tesla sedan.
To brake as fast as the traction limit on the tires, which is what you get from disc brakes, you would need four wheel drive and then bigger than normal electric motors and everything else to be able to absorb that much power that fast.
And then the battery would get really hot, especially if it was small.
It would be nice to see a track focused version with half the battery capacity. Take advantage of the reduced pack volume and shorten the wheelbase for additional weight loss, now the weight can be on par with an ICE Lotus. RWD with CoG behind centerline and tighter polar moment than an Elise on top of EV torque sounds like an absolute handful; call it a Evropa and have some fun at the local autocross!