I'll try to answer some questions posed here.
1) Yes, the optimal dry traction with a given tire is with minimum void area for maximum surface area at the tire-road interface. Unlike the physics of friction between solid, hard objects (where surface area is NOT an issue and greater surface area does not increase the overall friction, rubber is an elastic malleable substance and a large part of its traction is dependent on what is called in the industry, the 'rubber interlock'. This is where the rubber molds itself to the imperfections and irregularities in the surface. Softer rubber molds to the surface better, but if it gets TOO soft, then the rubber nubs extending into the microscopic depressions in the surface can shear which results in lower grip.
2) A bald tire and a slick are NOT the same thing. Racing tires and R-compound tires are designed with a minimum of void area so there is a maximum amount of rubber contacting the road for the greatest grip. As someone else has mentioned, racers will sometimes shave the tires for a shallower depth to increase grip AND service life of the tire. This has to do with heat buildup in the tires. A rolling tire inherently builds up heat. This is due to both the rolling friction with the road, and from internal stresses in the rubber as it deforms while rolling on a hard surface.
Shaving the tires reduces the amount of deformation (what racers feel as and call tire squirm) AND the shallower thickness of the rubber aids in dissipation of the heat buildup in the tires. A given rubber compound has an optimal operating temperature range to provide maximum traction. Below this optimal temp range, the rubber is too hard to fully conform to the surface irregularities to provide maximum grip. Above the optimal temp range, the rubber becomes too soft and wears and shears more easily also reducing max traction (what racers call overdriving or overheating the tires). The reason shaving increases grip and tire life in racing slicks is due to lower heat buildup and reduced deformation. Thicker rubber deforming more under hard lateral loads can cause a phenomenon called chunking where chunks of tread break off.
On a sidenote, because a tire's max traction is achieved at an optimal temp range, it IS possible to 'overtire' a car. This is when a racer mounts tires that are significantly too wide for the car. Within reason, wider tires DO actually improve traction in all directions (braking, acceleration and lateral), but if the tires is much wider than the weight of the car is fit for, the light car may not cause enough deformation to keep the tire rubber in its optimal temp range, resulting in reduced maximum grip.
3) The reason a bald tire, worn down till there's no tread is NOT equal to a slick tire is due to several reasons. For one, all rubber tends to harden over time. This is dependent on the rubber's composition and the conditions it has been exposed to. With race compound rubber, this is known as the heat cycle life. The softer race compounds have a much shorter heat cycle life than street tires. A set of Hoosier race tires for instance, can heat cycle out in one weekend, even though the tires have enough tread/thickness left, the rubber compound has hardened so that they no longer provide the maximum traction levels as they did new. Street tires do not heat cycle out as quickly, but they still do. If you've ever seen a tire with lots of remaining tread but with visible cracks on the sidewalls, you've seen the evidence of this. Exposure to more heat cycles, exposure to UV (sunlight) and exposure to ozone all accelerate and exacerbate the rubber's deterioration.
For maximum dry traction, buy tires made for it as opposed to running regular tires till they're bald.
Max