It gets tricky because calculating calorie consumption is really hard (how much of what you ate was actually turned into energy) and calculating calorie expenditure is probably even harder.
Yes, hence "you have to balance your chemical equations", but we need to agree on what we're calling "eat" and "burn", here.
Burning 600 calories can just as well "work up an appetite" as it can "draw upon fat reserves".
We're used to thinking of weight loss as a behavioral problem withy metabolic symptoms ("he eats too much, so he got fat") whereas there's reason to consider it as a metabolic problem with behavioral symptoms ("the kind of food he eats signals to the body that fat should be created, so his body signals for him to eat more").
"It's a glandular problem," you'd often hear a few decades back. Now, there is other mumbo-jumbo. But, at the end of the day, fat people eat too much. Period. Mass is not created out of thin air. (Unless you're a plant.)
Whether this fact is "helpful" to people trying to lose weight, I'll leave to the psychologists. But, it's true. And, there are some fat people that do change their behavior when presented with the truth; namely, quit eating foods with so many carbs, starches, and sugars.
In the case of eating, you can control directly how many calories are coming in, and you have at least a little control over how many calories are going out. So in fact CICO is very often useful: it's a kind of promise that if you cut your intake sufficiently you will lose weight.
It's true that certain diets will make you want to eat more calories: but the promise of CICO is that if you ignore what you are inclined to do, and simply focus on your intake, you will lose weight.
Obviously you are better off adjusting your diet too, but that's because doing so makes it easier by burning slightly more calories and making you slightly less hungry. What you're doing is a sort of sociological analysis: figuring out why people eat too much. Sure, if you can come up with tricks to eat less that help dieters, that's great, but people who want to diet fundamentally have to learn to ignore the instinct to eat and limit their intake.
Because they are gluttons and lack self-control. Why coddle them?
Whether the body decides to use stored energy or lowers output (while signalling hunger) is mostly hormonally controlled, by insulin and glucagon - this is why insulin resistance is such a problem.
Some research seems to show that portion restriction leads to lowered output while increasing time between meals (i.e. not snacking) lead to use of reserves, but I don't have a nice article to link.
Simplifying it to calories in calories out is a generalism of a generalism.
Like I said, calculating both ends of the equation is tricky.
Which is weight loss and/or belt size loss.
And watch for side effects which may require dietary adjustments. (not necessarily caloric)
Variable you cannot control is relatively worthless. Focus on what you can control.
Also this is still calories in, calories out.
Address the core issue first before arguing about minutiae. The emphasis on relatively low impact factors is especially unhelpful and unhealthy because people latch onto all these discussions as justification for why they can’t lose weight. Sure, an obese person might have a low metabolism[1], but if they eat 3500 daily calories and live an entirely sedentary lifestyle, those are probably the major causes.
[1] But they don’t. Study after study have shown that obese individuals have high metabolism because metabolism is tightly correlated with total body mass.
Constantly talking about genetic predispositions, obscure metabolism suppressing viruses or gut flora does about jack shit to help people lose weight.
Your body doesn't care how the calories go out. If they're gone, they're gone. If you eat 3000, but crap out 2000, your body doesn't say "Yeah, well, that's not how you usually get rid of calories, so get fat."
Just because our methods of recording aren't perfect doesn't mean that the core idea is wrong.
If your metabolism goes down, so do the calories out. That's one of many reasons that counting the calories out is extremely difficult.
Reduced metabolism when dieting is a thing, and it's also correlated to weight loss. Less weight, less base metabolic rate. Down to a point which is irrelevant.