I think you’ve missed some key posts, or perhaps don’t want to hear the message?
Let me try to phrase this as simply as possible: Energy balance is the wrong lever to exert to get the body to lose weight. Whether you are on a high- or a low-carbohydrate diet, eating less and moving more will cause the body to lower your metabolism to compensate for the energy deficit. It’s why almost every weight-loss plan out there is unsustainable over the long-term. Eventually, the hunger gets to people.
Now, the key to letting fatty acids out of our fat cells is to eat in a way that lowers our insulin sufficiently, and for long enough at a time, for this to happen. The lever is not manipulating energy, but manipulating the body’s hormonal system (insulin is a hormone) to allow excess fat accumulation to be metabolized. Lowering insulin is what lets fatty acids out of our fat cells to be metabolized. The food that stimulates insulin secretion the most is carbohydrate, which is why we strongly recommend reducing your carbohydrate to a very low level (some people can do fine on more than our recommendation of a 20 g/day limit, but some people need an even lower carbohydrate limit in order to get their insulin down).
Protein stimulates insulin at about half the level of carbohydrate, but we must eat protein, so eat it and don’t worry about it. Fat has such a small effect on insulin that it is negligible. We recommend replacing your carbohydrate calories with fat instead. Since fat has twice the calories of carbohydrate, it takes less to satisfy us.
There is a further issue for those who have excess fat to lose, and that is that restricting calories causes the body to hang on to its reserves. The body will cannibalize muscle before it starts to metabolize its fat store, and someone with no body fat is far along in the process of starvation (which is why so many concentration camp survivors didn’t live long after rescue). So if you don’t want your metabolism to go down, you must give your body an adequate amount of energy.
Your fat cells produce a hormone called lectin, which is supposed to let the brain know that we have taken on a sufficient supply of energy and can safely stop eating. The brain is supposed to then stop ghrelin production (ghrelin is the hunger hormone), and when it does, we lose our appetite. That is our signal to stop eating. One of the reasons fat people are hungry all the time is that too much insulin occupies the leptin receptors in the brain, so the brain never gets the “stop eating” signal from the fat tissue and keeps on producing ghrelin. However, once insulin levels are reliably low again, the brain receptors stop being blocked, and the lectin starts getting through again.
It takes a few weeks on a well-formulated ketogenic diet for the brain to start registering leptin again, but when it does, the appetite is regulated according to the amount of energy available. If you have excess stored fat to lose, the appetite signaling will guide you to stop eating at a point that allows you to metabolize both the fat in your meals and some of the excess fat from your fat tissue. (As you lose your excess fat, of course, your appetite slowly increases until your food intake matches your energy expenditure, because you have no more excess stored fat to take advantage of.) But the point is that, while you have fat to lose, you will be eating at a caloric deficit, yes, because your expenditure is being met from both intake and energy reserves. But the lowered intake is natural and hormone-regulated, not predetermined and imposed on the body. For that reason, it does not trigger a slowdown of the metabolic rate.
In such a case it is not eating less that has caused the weight loss, it is putting your body in weight-loss mode that has caused you to eat less. I’m sure I already stated this in an earlier post in this thread, but it is a point that bears repeating.