F1 cars drive on virtually perfectly smooth roads. Therefore, smooth tires would have the best surface area on the smooth road.
Public roads not only are bumpy, but they have rocks, dirt, water, and ice. So a smooth tire would have less contact, and therefore less grip. So treads allow the tire to fall into the cracks and bumps and get more surface area.
In short, treads would be slippery on a smooth road, and smooth tired will be slippery on bumpy roads.
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