That's an oversimplification. Hormone response is not well-understood enough to make blanket statements like that, as far as I know.
There's been tons of research on diets. Low-carb high-protein diets certainly do work, but so do several other diets, including some of the traditional "eat less calories" diets (the research I've seen indicates those diets are on par with Atkins and keto in terms of long-term weight loss, and they all work when consistently/correctly applied). Reducing calories below resting metabolic rate demonstrably causes weight loss. It's almost impossible for it not to.
And, there are ways to manipulate insulin response without going to a high-protein/fat low-carb diet. I've been experimenting with intermittent fasting; where I eat mostly freely, but responsibly, for ~8 hours out of the day and fast the other ~16. This has been shown to improve insulin response, in similar ways to low-carb diets.
I've lost about 16 pounds over three months. Every few weeks, I change the diet, to see how my body responds, in terms of energy, weight, etc. And, also because I love food and really like variety (lots of weight loss programs suggest a very regimented diet of the same thing every day for months or years, but that's not for me).
I've found that when my calories are below my MR, I lose weight, no matter what I'm stuffing my face with. I did a couple of weeks of bread and pie and ice cream every day (to the point where I got tired of bread and pie and ice cream), and still lost weight during that time; calories were consistently below my MR. And, I did nothing but proteins, and healthy fats, and greens for a few weeks, too...also lost weight, but not notably more than the "bread and pie and ice cream" weeks.
I've kept logs of my weight and caloric intake for a couple of months, and it's pretty consistent. A couple days after I eat more calories than my MR, my weight either stabilizes or increases. And, a couple days after I return to below-MR, I see the weight dropping again. I will say that I've had better luck with intermittent fasting than with portion control as a means to achieve below-MR caloric intake; so maybe there's something to the insulin response theory since there's evidence fasting helps with that.
There may also be an argument to be made about cravings (sugar+fat can cause cravings; there's decent science on that), and that may lead to problems managing portions and caloric intake. And, there's certainly evidence that protein and fat calories are more satisfying than sugar or simple carb calories. It may very well be easier to lose weight on a high-protein and high-fat diet. But, when I was on the high-protein/high-fat diet, my cravings for fruit were pretty intense, and the weight loss was not measurably better than the other macronutrient mixes I've tried. I didn't find it valuable enough to continue, so I went back to eating rice, bread, and having dessert sometimes.
But, "eat less" still works, and always will. That's not really negotiable. The basic physics of the thing require it to work. It's just that a lot of folks have no idea what "eat less" really entails and don't keep track of what they eat well enough to know they're not actually doing it. When losing weight, you're going to experience hunger sometimes, which is not a thing modern people are accustomed to.