I'm enjoying this discussion!
However, I have a couple things to add.
First, the coefficient of friction isn't affected by the contact patch size, nor does it affect the normal force. Tire contact patch theoretically has nothing to do with the available friction at the tire. This theory is much easier to see on pavement though.
There are two reasons you see wider tires on performance vehicles. First, is wear. If a vehicle is driven hard, the tires wear quickly, and with a wider tire, there is more rubber there to wear down. Think of extreme cases... a very thin tire is going to wear down much quicker than a wide cylinder of a tire.
The second reason has to do with shear. As you know, when someone does a burnout, it leaves black marks. The tire is actually shearing away, or tearing, as Scott mentioned. With a larger contact patch, there is more material that must shear, and the shear force is spread over a greater cross section, thus making it harder for a tire to tear away, and thus makes sense for drags or street racing.
Our terrain is different though, as we can actually bite into our terrain. This leaves the terrain to shear. So again, if you are in a situation where you are spinning tires and kicking up terrain (sand, mud, snow (not ICE)), you could possibly benefit from a wider tire (or just a greater contact patch). Think of a 2WD baja vehicle or a Rally vehicle.
To me it seems to come down to a difference of speed. If you are traveling at high speeds, or traveling in lots of deep mud, sand, or snow, then a wider tire could be beneficial... However, the main expedition mode of travel is generally slower and over a varied terrain, which allows us to run a slightly narrower tire.
It seems to me that a narrower tire is always beneficial due to fit, aerodynamics, rolling resistance, steering force, etc... but narrow is all relative. It seems the rule of thumb is to go as narrow as possible for your specific application/terrain.
The alternative side is exactly as stated in posts above... if you go too narrow, you either have to lose sidewall, or lose stability. A tall narrow tire will experience much more waddle than a wider tire. Along the same school of thought... a tall narrow tire is also much more susceptible to popping beads when under a side load (turning or off camber).
So for every application there seems to be a happy medium between too tall and too narrow.
At least thats my point of view.