Not so. (Converted posted at the same time, so this doesn't reference his post)

The formula for calculating "static friction", does not have an "area" component.

Ff = uN

However, when a tyre is under load, the cross-section of the tyre does not have a uniform "static co-efficient of friction", as u (mew) changes with temperature, nor does the tyre have equal force (Newtons) on the crosssection of the tyre on the ground.

So as you can see, it's all rather complex.

The basic reason for having wider tyres is that they last longer (if both are same compound). There is more rubber supporting the load of the car, allowing the tyres to be softer, which changes the u (mew= static friction constant) to be more favourable to grip. The bigger tyres also dissapate the heat better, keeping the crosssectional tyre temperature more consistant.

I believe this is the best tyre explanation.

If tyres didn't get hot, skinny ones would be the best.