From years-ago physics: Materials absorb heat; the number is called "Specific Heat." The more heat absorbed, the higher the temperature of the material. But if you have twice as much material it will take twice as much heat energy to raise it to the same temperature.
So, yes, the thicker metal wastes wood. It takes more wood to raise it to a given temperature vs thinner metal. It also takes longer to cool down. The energy to reach the desired temperature is wasted during the cool-down. Is this a big enough issue to matter? I have no idea. Probably not.
During the cook, the metal's temperature will not go down as much when the cooker is opened, but for a given amount of heat energy it will take longer to recover when the cooker is closed again. Is this good? Maybe. But the heat energy lost from the open cooker is approximately the same for thick and thin metal. It is only the temperature deviation that is different.
Thicker metal will corrode at the same rate as thinner metal, but since there is more of it, the cooker will take longer to rust out.
I like the Yoders because they are very well made and solid, but I do not own one because I see no reason why they would produce any better cue than my Camp Chef. As I wander the comps before judging time, I see a huge variety of cookers including a large number of drums. I think this is testimony that metal thickness doesn't matter much.
I'm not a physicist but what you say makes sense to me. One of the things I like about the Mak is the metal is thick enough to be substantial and not likely to rust through but not so thick that it takes a long time to heat up or cool down.