Great. That’s the way. Let your body determine what it’s metabolic rate will be. It will be different for all of us, based on our unique genetic inheritance and environment. 1000 kCal for one person may be too much, and 3000 for another may be not enough [although those people would be extreme outliers].
If, as you reduce calories, you become lethargic and hungry then it is a reasonable assumption that your body is not making up the difference from body fat. The biochemical mechanism is that when insulin is high, your body fat contributes less energy to your body’s calculus.
It is also true that people who don’t have a lot of body fat become hungry and lethargic when they reduce their calories. For the same reason - their body fat is not contributing.
If you gain weight when you eat more than a set amount of calories then that is because it is above the metabolic rate your body has decided to run at that day.
Some people when their bodies have more energy they engage in wasteful uses of energy to burn it off - like heating the body, or ramping up the immune response, or even just involntary twitching (eg: crazy legs). So for them their metabolic rate increases when they eat more energy.
For other people just a little more energy than they need, and their bodies store it eagerly. I suspect that your basal level of insulin will determine where you fit on that continuum, because we know that insulin is a signal to hold energy in fat tissue and your basal level is how low you can usually get that.
Someone who has a normally very low level, or who has an endocrine system that is able to be very responsive based on food stimulants - likely sees their metabolic rate increase much more when they have more energy in the diet.
The biggest loser followup study showed that people who reduced their caloric intake beyond normal fueling signals (ie: eating less when they were still hungry) slowed their metabolism dramatically, and as long as they kept restricting intake it stayed slowed till the end of the study 6 years later.
I would like to see what happened to the BMR of any participants who switched to a low carb, fat to satiety diet … I suspect it would go back to their starting value. But Kevin Hall definitely doesn’t want to do that study.