You’re right, the most friction would be from a smooth tire on smooth pavement. (Or another high friction road surface). That’s why race cars use “slicks”. Tires with no tread.
Road cars need to be able to deal with rain, and wet roads, and sometimes snow. The entire design of tread is to use the tire as a pump, and move the water out from under the tire, allowing it to directly contact the road surface.
If you had a treaded tire and a non treaded tire, both made of the same rubber: on a dry road, the smooth tire would have more grip. On a wet road it would have very little, and would also hydroplane very easily.
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