More surface area is great! As long as all of it is actually in contact with the road.
Uneven road: only the highest part of the wheel is in contact. Dirt on the road: the dirt digs into the wheel, which shortens its lifetime. Water on the road: now the tire is in contact with compressed water, which is *much* less grippy.
Treads on tires fix all of those problems. Uneven road or dirt? Highest point/dirt either goes into a tread groove or the tread has enough flex to go around the obstruction. Water? Now compresses in the treads, instead of between the tire and the road.
F1 just has strict road maintenance and shorter tire lifetimes to avoid dealing with the many problems that come from smooth tires.
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