[Adam Y.]

If you relate this to the automotive industry, in most cases wider tires do have more traction, but this has little to do with contact patch width (as most wider tires, of the same OD, with the same tire pressure, have the same contact patch as the thin tires). Cars, for example, desire wider tires primarily because of composition, as well as temperature, side wall deflection, pressure allowances etc. It is not as simple as the commercial "wider is better" Wider tires of the same compound do not have more traction, but will usually have stiffer sidewalls which inherently have less roll and give better handling characteristics.

Actually your wrong. In very special cases wider tires will actually help traction. Race cars are one example of such a creation. Their tires are wider than an average cars. This is designed so that as the car races through the track the tires start to become gummy. This actually causes the tire to stick to the track.