Although this seems obvious it is rarely stressed in most training documents.
It is mentioned (indirectly) in places but you are right - it is not stressed. It is not stressed because it should be intuitive - if you could carry more by using the same amount of energy you would be violating basic laws of physics, last I checked all other forms of transportation require more energy to carry more cargo, it would be naive to think we could pull some sort of miracle in aviation. Wouldn't it be nice if 747 used less fuel than Cessna 172?