Often repeated but this part is not correct. With decent tires, differences in Hysteresis losses due to contact patch shape are not nearly so significant as people think, but this is not my point.

Even running equal pressure, the wider tire has almost the same length contact patch. But you run a wider tire at lower pressure (or else you loose most benefit), in which case the length of the contact patch is significantly longer. The tire casing flexes more, but real world testing indicates this is not a significant factor.

Smooth steel drum tests with contemporary performance tires say there is slightly more resistance with wider tires, but textured drums (tread plate) and real world tests say wider tires are clearly faster in terms of complete system rolling resistance.