Drag racers and pullers do need a bigger contact patch, but for different reasons.
For starters, frictional force between two surfaces is equal to the coefficient of friction multiplied by the normal force (force pushing the two surfaces together). Most of the time, the coefficient of friction is a constant for the pair of surfaces, so the frictional force is independent of contact area and increases proportionally to the normal force. Double the normal force and the frictional force doubles.
Rubber on asphalt is an odd case. As contact pressure goes up, the coefficient of friction decreases. Double the normal force and the frictional force doesn't quite double. Therefore, you can increase traction of tires on asphalt by increasing the contact area.
For pullers, it's an issue of shear strength of the soil they're pulling on. There's a limit to how much force the tire can exert on a square inch of the track before the upper layer of soil shears away from the track. In order to increase the pulling force, increase the square inches of soil being sheared away from the track.
For starters, frictional force between two surfaces is equal to the coefficient of friction multiplied by the normal force (force pushing the two surfaces together). Most of the time, the coefficient of friction is a constant for the pair of surfaces, so the frictional force is independent of contact area and increases proportionally to the normal force. Double the normal force and the frictional force doubles.
Rubber on asphalt is an odd case. As contact pressure goes up, the coefficient of friction decreases. Double the normal force and the frictional force doesn't quite double. Therefore, you can increase traction of tires on asphalt by increasing the contact area.
For pullers, it's an issue of shear strength of the soil they're pulling on. There's a limit to how much force the tire can exert on a square inch of the track before the upper layer of soil shears away from the track. In order to increase the pulling force, increase the square inches of soil being sheared away from the track.