On car tires, shoes and other such items, having less of the material in contact with the surface underneath increases traction. Why is that? Isn’t friction a function of the contacting area and speed?
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On a smooth, dry surface, you are correct, a smooth tire increases traction due to maximizing contact with the road. On an uneven surface, a wet surface, or a loose surface such as dirt, tread patterns increase the surface area in contact with the road when compared to a smooth tire. Tread patters can additionally contain channeling to allow water to flow through the tread instead of sitting between the tire and the road, increasing traction in that way.
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