The more I think about the question asked here, the more I get confused. There isn't going to be a magic wheel that's fat and weighs the same as a race bike wheel. Trying to think about that premise is making my head hurt.
What works best just depends on the conditions. A quick test with two similar CA equipped bikes shows how a wide tire rolls better in soft dirt, sand, mud. The deeper the rut the more power it took to dig that deeper rut. Floating over the top uses lots less energy. But if it's bottomless sugar, all tires short of ATV tires may sink in and suck amps.
But to look at rolling resistance, go back to horse power. Back in the day, a wagon wheel was 3-4 feet tall. Two reasons, one being rolling resistance. But it was rolling resistance over rocks, logs, stumps. Not smooth road. Also, the tire was steel, so narrow was cheaper, and weighed less. It would cut to the bottom of a deep mud hole, and leave the axle above the ground. So it needed to be tall.
It was still horse and buggy days when the safety bike came out, and roads sucked. Wheels were big for good reason, as they still are for off road bicycles. But add enough power, and the need for that big wheel diminishes. Motorcycles and quads don't require a 29er wheel to handle rough stuff.