Idealized = contact area is just a "perfectly" thin line and there are no deformations.
Also, wider tires will reduce the stress per unit area of each tire - that's why you can corner easier with wider tyres when driving high-speed, less because of higher friction. Narrower tyres would be too stressed and blow.
All very true. The application of softer compounds b/c of reduced load as well. But that is beside the point.
Even if you had two examples of the same car, with same compund tyres, but one had tyres twice as wide, it would have more traction. Or if you had the same two cars again and made one half as heavy, it would corner faster. The point is, lower contact patch pressure means a _higher_ friction coefficient, regardless of compund.
Coulomb's law(F=uN) as taught in high school is not an actual physical law, it's an empirical approximation. A rule of thumb, if you will. It doesn't apply for everything in all circumstances, especially tyres in this case. And then we haven't even begun to model stuff like adhesion, dynamic friction, slip rates et.c...
http://www.racecar-engineering.com/images/features/asymmetricalracecars1.pdf