My experience - low pressure is harder to roll. I have a slow leak in one tire that I have to keep an eye on because on all surfaces, that side is harder to roll when it gets low.

From the physics side - more surface area of contact between a surface and a tire (spreading the load, as you say) creates more friction. This is good for cars, as more friction means better traction - wider is better. But increased force is needed to roll a wider tire that "holds the road" better.