Rather, you are rewarded for driving dangerously and taking down your opponents (and chasers) by any means necessary.
In the racers career mode, you are not rewarded for doing stunts or crashing in a spectacular manner. The option to be able to play as both an illegal racer and cops brings both variation and variety to the action of the game. Cops have access to stronger vehicles (good for taking down illegal racers in their lightweight cars) while the racers have faster cars (good for eluding cops who aim to shut them down). Both career modes have their own unique set of cars and equipment. There are two career modes that the player has access to: racers & cops. Unless you are in free-drive mode then you can drive wherever you please. So it could be considered open-world in a loose sense as you are able to take shortcuts when you are able too, but constrained to the race route. Need for Speed: Hot Pursuit takes place in the fictional Seacrest County, with over 100 miles (160 km) of open road for players to race on.
Unfortunately the game doesn’t seem to cooperate with my Xbox anymore so I ended up buying a new copy for the PC instead. Admittedly, my console is rather neglected but I did remember enjoying the game immensely. Need for Speed: Hot Pursuit was actually one of the first games I bought for the Xbox 360.