I'm not sure what your problem with this method is, given that the amount of heat given by burning is the definition of a food calorie.
That's like saying "once I learned that voltage was measured by the deflection of a coil in a current (a practice started in the 1800s)" or "once I learned that heat was measured by the expansion of a liquid in a glass tube..."
You could argue that the heat definition of calorie doesn't really reflect the health function of the food (for example, maybe glycemic index is more useful), but I'm not sure why complaining that a calorie isn't a calorie is really insightful.
My problem with this method is that my body does not burn the food in the same way. And, it doesn't burn every food in a way similar to every other food.
I get that it's the best scientists could think of 100+ years ago. But putting averaged numbers derived from this absurd method on labels as if they are how my (!!) body works, and deriving all kinds of "food science" conclusions and recommendations from it is imo willful ignorance in the name of convenience.
Your body isn't actually burning the food. Therefore, why is this an important measure, other than it is easy to measure?
Bioavailability / metabolizable energy varies not only in the small, ie composition and cooking of food, but in the large, as long run diet choice changes gene expression.
Actually, respiration is burning the food, it's literally the same energy release, and the methods of calculation take into account the portion of the food that's burnable but non-digestable. If you're saying that the corrections for indigestible food are the subject of scrutiny, that's true, but that has nothing to do with the fact that "burning" is a problem for calculating caloric content.
I used to work in aquaculture, where we measured the amount of food going into a fish (via the bomb calorimetry that we're talking about, directly), the amount of energy spent by the fish in respiration (by measuring carefully increases in water temperature in their tank), and then we measured how much energy the fish had at the end (by burning the fish).
And quite simply, calories in was equal to calories out. It was a good relationship within very acceptable experimental error.
Now of course, the fish were growing very rapidly and we could control their food exactly. Humans, growing over a longer period, can be subject to different metabolic pathways, and we can't measure their respiration directly of these pathways [Edit: this is where the gene expression you mention comes in] - this is a far, far bigger source of error than the calorimetry, so calories alone can be less predictive of outcome. But this doesn't take away from the basic definitions of thermodynamics.
1) respiration is burning the food, but it's not burning all the food; "calories in" refers to calories absorbed, not calories put in your mouth; and the proportion between those two varies depending on all kinds of things, including e.g. gut microbiome and temporary changes to that due to various drugs; so if you strictly count calories put in mouth you still get a hard-to-measure variability in actual "calories in" (unless you put a respirator on the subject and measure it that way).
2) All other things being equal, changing "calories in" will make you lose/gain weight. The trouble is, all other things are not equal - simply changing how much you eat will significantly change those other things, it has an effect on your metabolism and eagerness for physical activity, thus directly affecting also "calories out" if you don't carefully monitor that and work to keep that stable.
3) All other things being equal, changing "calories out" will make you lose/gain weight. The trouble is, all other things are not equal - simply starting/stopping working out will significantly change your natural appetite, how hungry you are and how often you're hungry, and which types of food you have cravings for, thus directly affecting "calories in" unless you carefully track what and how much you eat everything and actually do keep that schedule exactly the same.
Ok but if my body takes for example an amino acid and uses it as a building block for repairing a muscle, that building block hasn't been burned, correct? So that "calorie" is functioning in a completely different way than as an energy source.
It's like we didn't burn the wood or store it for fuel, we used it to repair the walls of the house.
Yep. Though it's still counted as a "calorie" that's stored in your body as a certain number of grams of protein. If your body later decides to lose that muscle, then the calorie is spent.
Since fat and protein each have different amounts of calories stored per gram, that's why if you want to get really accurate about weight loss/gain, you track your body's %fat & %muscle and not just your weight.
Edit: to clarify your analogy, just because we use wood to build a part of the house, doesn't mean we won't take it and burn it if we're desperate for heat and have used all the other fuel.
Are we accepting that the complex biochemical mechanisms of the cells are identical to burning things in an open flame?
And, that every living human's body processes all foods in exactly the same way, regardless of age, ethnicity, gender, time of day etc? Just like the open flame would?
That's like saying "once I learned that voltage was measured by the deflection of a coil in a current (a practice started in the 1800s)" or "once I learned that heat was measured by the expansion of a liquid in a glass tube..."
You could argue that the heat definition of calorie doesn't really reflect the health function of the food (for example, maybe glycemic index is more useful), but I'm not sure why complaining that a calorie isn't a calorie is really insightful.