Just to reinforce the brakes message: The braking power on the Bugatti Veyron is in excess of 1.1 megawatts. Braking requires 30% more power than accelerating.
>be very difficult to connect to a powerful cooling system. Even electric motorcycles with 30-40 bhp rely on water cooling, let alone a car 20 times the weight.
This is true- Teslas besides the model 3 and several bikes use liquid cooling. I want to point out that this is not a necessity for motors <200 kW though. Manufacturers are uniformly switching to IPM motors (aka PM synchronous reluctance motors), including Tesla. These motors are much more efficient and allow for cooler high power operation. For instance the Chevy Bolt's 150 kW motor (a weird but decent design) is fully enclosed and cooled pretty much passively.
Previous motors were either inefficient at high power (induction motors) or inefficient at low power (PM motors)- in order to reach low-power efficiency they had to be undersized and required extreme cooling to reach high power.