I never said or implied that humans can interchange nutrients from one form to another because of conservation of energy, there's plenty of examples of chemical energy that the human body can't do anything with. That isn't related in any way to the point I am trying to make.

I don't think I communicated clearly what I was trying to say, so I'll restate it:

You are right that merely considering estimated calorie intake, and estimated calorie expenditure is a drastically over-simplified model of what's going on that fails to account for many things.

However, it's accurate enough to meaningfully model weight loss in humans. When someone switches to a paleo diet and is losing 2lb/week (as happened to me for a solid 6 months when I did), it's not because they're using lots of energy by some mechanism not accounted for in the over-simplified calories in/calories out model.

If you estimate food intake, you will find that a person losing 2lb/week on a paleo diet is in fact eating roughly 7000kcals a week less food than they used to.

The paleo diet doesn't cause some metabolic condition under which the estimated calories in/calories out model is drastically inaccurate: it primarily causes overweight people to eat much less food.