I definitely agree that we have tons of great food options out there that do not involve added sugar! Lots of foods have natural sugars, so it's always a balancing act to find items that are nutritious but low in sugars.
I do agree that fats help you to feel full. I tend to feel full when I eat because I drink a lot of water with my meal, and drink a lot of water in general. So I really don't need a lot of fat to "feel full" or to feel satiated. Also, stomachs shrink as your size does, so really you don't need to eat that much to feel full, as you lose the weight.
Definitely if you let your body get too many carbs / sugars in it, it starts to crave them which sets up an endless cycle. Like Chinese food

You get the sugar high, then the sugar low, then you want more sugar.
Really, when you come down to it, there are only four energy sources out there that a body can burn. They are carbs, fats, proteins and alcohol. That's a simple biology fact. We don't recommend living on alcohol

And since we're trying to cut out carbs, that leaves us with proteins and fats. You are leaning heavily in the fat direction. I'd probably be at least half-half protein-fat in my balance, but if you really do get enough nutrition and protein in you every day, and you are active enough that you burn them off, then it sounds like your mix works well for you.