I don't think that willpower is the problem for most people. It's what they are eating. Obviously the amount of what they are eating is a factor, too, but most importantly it's the "what" part.
For this statement to be true, it must *always* be true. I propose to you this concept:
Person A eats 1500 calories a day of nuts, fruit, veggies, and bread. Lets say the fruit and bread account for half or more. Maybe even ~300 calories of nutella a day on that bread.
Person B eats 4000 calories of keto-friendly stuff.
Who loses body mass? Only an idiot would say person B, and that's my point. I know you don't think Person B does.
What you eat is certainly important. It's extremely important to being healthy while losing weight. If you cut down to 1400-1800 calories and eat shit, you will feel like crap and probably fail the diet. It's a really important component, but this is so common sense that I don't think it even registers as something that needs to be explained.
But so many people think that eating healthy is the key. It's not. I ate really healthy while I was at 280-300 pounds, it was just that I ate a lot of it. Portions and calories are the essence of weight loss. What you eat in that reduced calorie amount is very important to maintaining that diet, but that's step B.
You can eat like shit and lose weight as long as calories are down. It might be unhealthy, but you *will* lose weight. You can't eat a ton of healthy food and lose weight.