There is no question that significantly reduced food intake over the long term results in weight loss. However, consider that those of use trying to lose weight are more concerned with fat loss without concomitant loss of muscle and bone, and for the purposes of improved health, not starvation.
Most people want to be able to eat a reasonable amount of food and maintain a stable, healthy weight. So the trick is - how to reduce food intake in such a way that we lose primarily fat tissue, retain muscle tissue, and don’t trigger a significant reduction in metabolism which confounds the weight loss goal?
I think in an otherwise metabolically healthy person who is not significantly above their optimal weight, a simple change in the calorie equation (such as - reducing intake by 250 calories per day and increasing output by 250 calories per day) would let them lose a pound a week or so without having to make any other real changes. That 250 calories is about 2 ounces of carbs or proteins, or about 1 oz of fat, so it’s easy to miss that target unless you are very careful about weighing and tracking everything.
Back to the original question - if I were to eat a low carb, moderate protein, high fat diet, and get all of my body’s energy needs from my food intake, there would be no reason for my body to burn any stored fat. I am going to have to create a food-intake deficit to get my body to look for energy elsewhere - in the form of existing storage. So assuming I don’t vary the carb or protein significantly, then yes, I have to cut back on fat intake since that is the only macro that I am varying.