If you read through the article I posted a link to, it concludes that wider tires primarily are for wear reasons. As we all know, a rubber tire sacrifices itself to provide the friction (all the gum balls on your front tire after a track session prove this is so). A small tire dealing with significant friction demands, and in drag racing probably being overloaded will wear fast. So if you had the smallest tires that could support the weight of the car and did a run, you would likely destroy them due to friction heat and mechanical stress. If you were really serious about winning a drag, you could have single pass tires that had just enough strength for a run and then die. They would be smaller and lighter. But you would change tires every single pass. So the extra rubber is for wear and handling of forces - vertical, lateral, roll on the sidewalls/carcass, flex to absorb acceleration and deceleration shock, bumps and so on. It doesn't provide more friction or grip.