[Clev]

When a tire is under-inflated, the shape of its footprint and the pressure it exerts on the road surface are both altered, especially on wet surfaces. An under-inflated tire has a larger footprint than a properly inflated tire. Although the larger footprint results in an increase in rolling resistance on dry road surfaces due to increased friction between the tire and the road surface, it also reduces the tire load per unit area. On dry road surfaces, the countervailing effects of a larger footprint and reduced load per unit of area nearly offset each other, with the result that the vehicle's stopping distance performance is only mildly affected by under-inflation.

On wet surfaces, however, under-inflation typically increases stopping distance for several reasons. First, as noted above, the larger tire footprint provides less tire load per area than a smaller footprint. Second, since the limits of adhesion are lower and achieved earlier on a wet surface than on a dry surface, a tire with a larger footprint, given the same load, is likely to slide earlier than the same tire with a smaller footprint because of the lower load per footprint area. The rolling resistance of an under-inflated tire on a wet surface is greater than the rolling resistance of the same tire properly-inflated on the same wet surface. This is because the slightly larger tire footprint on the under-inflated tire results in more rubber on the road and hence more friction to overcome. However, the rolling resistance of an under-inflated tire on a wet surface is less than the rolling resistance of the same under-inflated tire on a dry surface because of the reduced friction caused by the thin film of water between the tire and the road surface. The less tire load per area and lower limits of adhesion of an under-inflated tire on a wet surface are enough to overcome the increased friction caused by the larger footprint of the under-inflated tire. Hence, under-inflated tires cause longer stopping distance on wet surfaces than properly-inflated tires.

Quoted from NHTSA (Tire Pressure Monitoring Final Rule(Part III)), bolding is mine.

Taking the above to its logical conclusion, inflating tires higher than placard makes the contact patch even a bit smaller, which would not increase stopping distances.