Tire rolling resistance question

Perhaps a stupid question but I’ll shoot my shot.

So the typically bit I hear is that wider tires are faster because they can afford to use a more supple casing, etc. One thing I don’t hear mentioned is that wider tires (especially MTB tires) are also taller, leading to a larger circumference. For example, the circumference of a set of my Peyotes is about 5% larger than the circumference of a set of my G One Rs 45s. Circumference seems to change even between G One Rs 45, 50, 55.

My understanding is that in a lab test, a larger circumference tire would be more efficient than a smaller circumference tire, all else being equal. If I understand the lab rolling resistance protocol correctly, it seems like that efficiency would manifest in the rolling resistance coefficient.

My question is, has there been any testing to differentiate the effect of a more supple casing from a larger circumference tire? Saying wider tires are faster because of a more supple casing seems to overlook the larger circumferences of these wider tires.