Here is a BRIEF description about what tires do at drag races, such as top fuel.
1. Car with cold rear tires does a rolling burnout way past the traps.
2. Rubber gets laid down on the track for about 10-15 yards.
3. Tires get warm in the process.
4. A wide patch of sticky hot rubber contacting another surface of sticky rubber causes a very high mount of friction. This friction helps to transfer the power to the ground causing the vehicle to move forward.
Dan, back to the "box theory". I do understand about weight distribution and how the larger contact patch will still have the same weight (lbs/square in.) but, that's not the goal of drag racing tires. We are talking about the physical properties of the rubber. A wider tire will give more friction to the tire relative to the ground.
You have to look at a few different variables when finding the right drag tire/wheel combo.
1. "Stickiness" of the rubber compound.
2. Amount of power going to be tranferred through the wheels.
3. Downforce applied to the wheels at launch (vehicle weight, distribution, and suspension are factored in)
4. Diameter of the tire and of the rim (see Terry's Slip Angle)
5. Road surface (composition, temperature, slope, etc.)
6. Tire pressure and temperature
This could get into a REALLY large, and probably heated, discussion.
One thing to think about when discussing tires and "grippiness".
There are two different states of the tire for observing friction: When it is slipping, and when it is not slipping.