There is truth in that protein has an important role in hunger signaling, but it’s not being well supported by the other claims you’re making.

over-eating fat or protein is very difficult - the body will simply be full

Fats are very easy to overeat though. I can chug a cup of olive oil in less than a minute and instantly meet my daily energy expenditure. I’ve never tried this myself because I would miss out on a lot of other nutrients, but I imagine I would be hungry again pretty soon afterwards.

With carbs, that drive blood glucose, and that drive insulin, eating anything will be used for anabolism (that is what insulin does)

Your body does a lot more with its energy than building new molecules. For example, ATP powers the movement of your muscles. So you could either consider ATP synthesis as anabolism, making this claim a non-sequitur (i.e. how does saying “carbs can be used to move muscle” support the claim of “low carbs will help you lose fat”?), or it’s not anabolism, in which case you’re just plain wrong.

Sadly calories are a useful lie, but not actually how the body works. Calories are how much energy is released in a tiny oven. The human body does not necessarily use everything that has a calorie attached to it.

No, we don’t use everything. But it is a useful way of measuring what we do use for the purposes of weight control. It’s trivial to verify for yourself. Just count the Calories in everything you eat and see that your weight gains and losses are very closely tied to that number. So it is indeed a “lie” in that sense that the number you see probably isn’t actually what your body is burning, and “useful” in the sense that it will tell you whether you’ll gain or lose weight. I assume that’s how you got to calling it a “useful lie”. I just don’t see how that justifies your stance that no one should have to count Calories.