The more rubber on the road the better, nice soft sticky rubber, hot, hot, hot. Darned good. But - it wears out quickly and has a higher rolling resistance. Dragsters for example, masses of power and the limiting factor is the coefficient of friction between the rubber and the road, the ratio between the force necessary to move one surface horizontally over another and the pressure between the two surfaces - as high as possible.
But that assumes a nice hard surface.
A soft surface or a crumbly surface will require more than simply surface area as the surface itself is unstable, so nice bobbly lumps on the tire help it grip between the loose stuff.
When I worked at Alfa Romeo in Italy - looong time ago - on our TT33, http://commons.wikimedia.org/wiki/Fi...red_vr_TCE.jpg, I built mathematical models of suspensions systems, both production and sport, we had a computer program that computed the actual contact area of a tire and the road, it used weight, pressure, wheel width which varied from 14" to 17" in them days, tire material and the relative position of the tire to the road. It them plotted how that area would move when the front wheels turned left and right, its position relative to the wheel was important to overall handling. Not so with a bike which leans and the moment exerts completely different pressures on the tire and wheel. Never worked on bikes.
Depending on whether the surface was concrete or blacktop or whatever, and how it was finished, whether it was wet or dry and the temperature, we would have a range of wheels with different tire material that best suited the surface. Pressure was adjusted appropriately and in some case suspension adjustment points were made to get the best behavior.
How I loved that car!
I ride my bike on Schwalbe 20" at 120 lbs. My goal is to reduce rolling resistance to a minimum. As to all the rest - to heck with it!
It really has very little to do with contact area. Basic friction mechanic tell us that the larger the area, the less pressure, the less pressure the less friction per area. What is really going on is that tires change friction characteristics based on load. The higher the load per area, the lower the friction coefficient that the tire produces. The other thing I remember feeding into it was slip angle, and wider tires had an advantage in preventing the tire from going outside optimum slip angle.