If you read Gary Taube’s “Good Calories, Bad Calories” he runs through the extensive history in weight loss and obesity research. The gist is, which is shown in study after study with both animals and humans, your body is “deranged” in how in uses and stores energy. Hormones play a huge role. There are studies that show people on a starvation diet of something like 800 calories with macro ratios more like the SAD that lose a bit of weight but are miserable and even result in self mutilation in some of the studies, while another group eating closer to 2,000 but HFLC and they lose several times more weight and report not being hungry at all. This is shown over and over again throughout history, but is still largely ignored by the mainstream.
The argument that people like to use is the first law of thermodynamics and the conservation of energy, which is the basis for the CICO argument. The 30,000’ view is ultimately energy in and energy out. However, the problem is, the human body is not a closed system and variables are not indepent variables. This is to say that your body wants to be in homeostasis. So, if you have a derangement that affects how and where you store fat, if you simply reduce calories your body will respond by reducing your BMR to try and maintain your weight. Look at the article that @carolT posted above. This is why calorie reduction will “work” in the short term, but it will eventually snowball and your BMR will reduce far enough that you simply can’t stand to eat any less and then you get stuck, fall off the wagon and the weight comes back and since you temporarily slowed your BMR, often the weight comes back even more before you hit that level of homeostasis.
The opposite is true, if you are predisposed to being thin and try and gain a bunch of weight by eating in excess, your body will respond by increasing your BMR and your desire to burn more energy.
But like I said, hormones play a huge role, which is where the ketogenic and other low-carb diets come in. Insulin is the hormone most responsible for what your body does with its energy that you intake. So, when you reduce your insulin levels (by removing carbohydrates) but keep calories the same (by replacing the carbs with fat) your body is more or less forced into behaving “normally” because insulin isn’t there to bully your cells into storing that energy as fat. So, in the absence of excess insulin your body does the normal thing and increases your BMR when there is an excess of energy and vice versa.
Reduced calorie SAD won’t induce ketosis because the glucose levels and thus insulin levels are simply too high, so it will never work in the long term as a solution to weight loss unless the person is willing to be miserable and voraciously hungry all of the time.
I’m sure this was a gross oversimplification of how it all works, but it is how I’ve explained it to people who’ve asked me in the past and I think they were able to follow along, so I hope this helped!