Smooth tires provide much less traction than those with treads. While this can be beneficial for racing cars, as discussed earlier, it is unacceptable for passenger cars, which must be able to safely brake and corner on a variety of surfaces.
Increased noise
Smooth tires would produce much more noise than those with treads, due to the lack of sound absorption provided by the treads.
Reduced fuel efficiency
Smooth tires would have less rolling resistance than those with treads, but this would come at the expense of fuel efficiency. The treads on tires help to reduce rolling resistance by providing a more consistent contact patch between the tire and the road.
Reduced safety
Smooth tires would be more likely to aquaplane, or lose contact with the road in wet conditions. They would also be more likely to skid on ice and snow.