Choice of macronutrient composition directly (and indirectly through hormones) affects satiety, and many find it easier to eat less calories by restricting carbs, but for weightloss at the end of the day a calorie is still a calorie.
Every pound of extra fat on your body comes from a calorie surplus that at one time or another existed in your bloodstream. If that surplus came from bacon or carrots doesn't matter for the pound of fat (it might matter for your heart and health in other ways of course).
It's also true that in order to lose that pound of fat, you need to create a deficit of calories in your bloodstream.
The problem is that you can't know how many calories from various foods actually end up in your bloodstream in advance. Just like any given number of "calories per hour of running" is obviously just a rough estimate (varies by how heavy you are, how cold it is, if it's uphill, how good a runner you are and so on), the number of "calories per serving" on the box of food is also an estimate.
Your body could be particularly good at absorbing calories from rice, or particularly bad at absorbing calories from beans. This could also be temporary, or affected by what other things you eat, or when you eat during the day.
The hackers diet solves this complex thing by having you keep a record of what you eat and do over time, and /measuring the results/. Then you know what is true /for you/, personally, and you can adjust your habits and predict the results.
The best tip I got from it however was the idea that hunger is a signal telling your body to start burning fat. That made me able to endure the periods of hunger during the first few days without giving up. Once the body started to burn fat, all the discomforts of hunger went away permanently for the duration of the diet. I think a lot of dieters fail just because they think the discomfort is unbearable and will last forever.
(This is for people with normal metabolisms, ie not diabetics)
Citation? My experience is consistent with yours. However, my understanding is that insulin is mainly a signal to cells to take on nutrients, and it is not exclusively a response to carbohydrates, much less "excess carbohydrates." Certain amino acids provoke an insulin response, for example. https://pubmed.ncbi.nlm.nih.gov/2660133/
I've also tried low-carb twice, the first time I lost a reasonable amount pretty quickly, but gained it back over a few years when I reverted to a normal diet, and the second time when I shifted to intermittent fasting as I went back to a more normal diet.
There's lots of good advice available if you search for intermittent fasting, but the key take away is that insulin is produced in response to excess carbohydrates, and not only promotes storage of carbohydrates as fat, but also inhibits burning existing fat. Of course, if you are at a calorie deficit, you'll probably still lose weight especially with regular small amounts, because the insulin effect will be low, but if you have few carb-heavy meals, your body will still create a lot of insulin to get rid of all the carbs, and then after you work through the hunger phase after that's happened, then you will start converting that fat back to energy, and in a calorie restriction situation hopefully burn more than you need.