Stiffness in a tire is bad. That's why more expensive tires are suppler. Energy lost due to rolling resistance on a paved road is primarily viscous dissipation

Stiffness in a tire is bad. That's why more expensive tires are suppler. Energy lost due to rolling resistance on a paved road is primarily viscous dissipation due to flex of the tire. If the tire is a stiffer material, this dissipates more energy. In addition, suppler tires deform over obstacles more readily, reducing bouncing and vibration. More or less, your contact patch is pressure/weight, since the tire can't support much weight on its own. It's going to be almost the same no matter what (slick) tire you are running. Wider tires have less rolling resistance for the same pressure (to a point), since the tire deflects less to maintain the same contact patch. Two tires of the same width, one stiff and one supple, will have to bend in the same way, and have nearly identical contact patches. However, the supple one will dissipate less heat doing this.