Interestingly, they race electric motorcycles at the Isle of Mann TT, and the riders all talk about how it's a different game to racing fuel-powered bikes - the bikes are capable of using up all their energy much more quickly that a fuel powered bike, so it becomes as much an efficiency trial as a race, they need to manage their energy consumption to ensure they make it to the finish line (all while still averaging over 100mph around the 40-odd mile mountain racecourse...)

I meant the limit as battery / bike -> infinity for a fixed race length, not the limit as distance goes to infinity. In the latter case, the human dies as surely as the car. The race stages are only about 200k, which is no problem for the car, especially at the relatively low speeds of the bikes.