Auto racing tires tend to be soft because that generates more friction. Unfortunately soft materials have weak shear strenth, so a large area is needed to support large tangential forces. (In effect, the amount of force that friction can exert is limited by the shear strength of the materials.)
Moreover, in some kinds of racing the vertical load on the tires due to wings is quite large as well, so the tires must be able to support much larger loads than the weight of the car which is also helped by the larger tire area.
Wider tires provide more resistance to slippery spots or grit on the road. Race tracks have gravel, dust, rubber beads and oil on them in spots that limit traction. By covering a larger width, the tires can handle small problems like that better.
Wider tires have improved wear characteristics. In order to achive maximum traction, the tires are made with materials that ablate as the car runs through the race - which is why the tires get switched so often. Narrower tires would wear out more quickly.
Remeber that car racing is essentially limited by the amount of friction that the tires provide. In other types of racing - like bycicle racing or track - where power is not effectively unlimited, the contact surfaces tend to be narrow and stiff for better efficiency.