If anything it takes less power to stop just as fast as you accelerate because of this wonderful thing called the atmosphere.
The problem is that stopping as fast as you accelerate is still too slow to be satisfactory in a lot of cases.
On low end cars that don't have enough power to roast the tires at any speed in any gear you need more braking power than engine power because you need to be able to use 100% of available traction to get from 60-0 for obvious "think of the children" reasons.
Nobody cares if your Yaris doesn't have enough engine to use every available bit of traction to get from 0-60.
Basically "you should be able to brake 30% harder than you accelerate" is a good rule of thumb for economy cars.
When you start talking high horsepower to weight ratios or other vehicular "extremes" rules of thumb don't really work.
Electric motors can be used to provide some braking via regeneration, but even so braking generally comes down to "how much heat can you dissipate". A small, slow (relatively speaking) city car won't have as much heat to dissipate, so there are more options when braking.
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.