When I control my food supply, my hunger will almost always override the cold math of the calories.
It's a bit like how abstinence can prevent pregnancies, so you don't need condoms or pills. It's of course true in a technical sense, but real world people aren't strong enough to remain abstinent.
That's a case of your hunger causing you to eat more calories, not a case of your hunger causing you to gain more weight from the same calories. The math still works just fine if you count the calories that your plan says you shouldn't have eaten. It's the plan that isn't working for you, not the math.
Sure, there are "tricks" (such as eating lots more low-calorie-dense food such as broccoli or cucumbers to quell hunger pangs) but those are just tools that still require hard work to apply.
A lot of people lose weight doing that without the hard work, aside from abstaining from all your favorite sugary foods. But there is plenty of delicious fat & protein food.
But yes, one of the driving factors of "hunger" (when people eat high-sugar foods) is the insulin spike and associated cravings. Cutting out all carbs gets rid of sugar, which results in no more insulin-spike-driven "hunger". But really, all you needed to do to do that was to reduce your sugar intake. It's also quite hard (though definitely not impossible) to load up on lots of calories without carbs. Most high-calorie food is also high in carbs, because refined carbohydrates are ridiculously calorie dense and it's hard to find something that's easy to eat lots of that matches it. You can't really eat a whole tub of butter, but you can eat a whole loaf of bread or plate of pasta.
> aside from abstaining from all your favorite sugary foods
That is the hard work I was referring to. While it might be a slog when you start out, exercise can be surprisingly addictive thanks to the rush of endorphins you get. But you don't need to exercise to lose weight, nor is exercise alone sufficient -- you can't out-exercise a bad diet.
Back when I switched to the paleo diet some 10 years ago, I was ready for a huge fight with my cravings as I gave up all the sugar and grains etc. But nothing of the kind happened. I just started eating other food that I liked just as much, and felt fine. Lost 25 pounds over 6-9 months.
Maybe it was unusually easy for me. And paleo does allow some carbs, though I definitely cut down a lot.
Agree 100% about your exercise point!