After thinking about this a little more I have some additional thoughts.

It makes a difference if a person is trying to lose weight or is just doing the diet to eat more healthy.

When a person reduces the carbs in the diet the calories that were going to energy from the carbs has to be replaced by something. As an aside adequate protein is good for the body as a building block but not a particularly good energy source. The body only uses protein for energy sparingly or if there are not enough fat or carbs to use. So replacing carb calories with lean meat is not the solution. Protein IS very important though, especially as we get older because our body does not process protein as efficiently, So to keep up lean body mass (our muscles) as we age keeping protein intake up is important. Dr Ben Bikman (researcher who specializes in insulin) is big on not restricting protein too much as we get older. But I digress. Back to fat.

For a normal weight person that is trying to not lose weight this means that whatever carbs are cut out of the diet enough fat needs to be eaten to replace it or the diet will become a calorie restricted diet. If calories are restricted the body goes into conservation mode and lowers its metabolism. This can cause a person to feel tired, cold and potentially hungry. So it is important to have enough fat in the diet. Fatty meat, egg yolks, avocado, etc.

For a person trying to lose weight it is a little different. They also will need to burn more fat when the carbs are restricted, but ideally that fat mostly comes from body fat that has been stored up for perhaps years. So they don't need as much fat intake from food because they are going to be utilizing body fat. There is a caveat though. Often (not always but most of the time) an overweight person is insulin resistant and has trouble accessing the body fat to burn. It is the reason they are overweight to begin with. So they have a little "training" to do of their body to access that stored up energy. First they have to get insulin levels low so they can begin to reverse their insulin resistance. That is where reducing the carbs to a low level comes in. Then, since their body is not accustomed to burning their body fat, they also need additional fat in the diet just like a normal weight person. This gets their body accustomed to being a "fat burner". Also it is very important to not drop the caloric intake in the beginning so the body does not go into conservation mode and lower its metabolism. A lower metabolic rate is counter productive to losing weight. For these reasons a person that is over weight in the beginning needs to up the fat in the diet just like a person that is not over weight. Then after a period of a few weeks of "fat adaptation" they will find that for once in their life their hunger has came under control. As they don't feel the need to eat all the time the natural progression is to not eat as often and their caloric intake will slowly drop over time. This slow adaptation will not signal the body to go into conservation mode so metabolism stays up. Then their body starts utilizing body fat instead of dietary fat and they lose weight.

Sometimes a person losing weight over a period of time will "stall out" in their weight loss pattern. Sometimes this then requires them to reduce their dietary intake of fat so they burn more of their body fat.

But in the beginning it is important to keep dietary fat intake up at least till the body becomes accustomed to fat being the primary fuel supply instead of carbs.

That is why it is important in the beginning to "not go hungry". Eat to satiety, but simply eat foods that contain fats instead of carbs. Once the hunger is curbed then a person can get away from the "snacks" all the time or perhaps drop back to two instead of three meals a day. "Being hungry" is ingrained into our brain as being a necessary part of losing weight while on a diet. But on a low carb or ketogenic diet reducing caloric intake (especially in the beginning) is counter productive. Now I eat like a horse and still do not gain weight. Last night I had probably a pound and a quarter hamburger steak (80-20 hamburger), a pile of bacon, some carmelized onions for the main course with a small apetizer meal ahead of it of mixed luncheon meats, radishes, half a boiled egg and a dozen olives (often times half an avocado but not last night). Plus home made yogurt (made from heavy cream, about 1/3 cup) with some chopped pecans and blueberries for desert. For lunch we had a breakfast type meal with me having 4 scrambled eggs with some chopped onion, three sausage patties, and a pile of bacon. I eat this much all the time with two meals a day and do not gain weight. Back when I was on carbs (with insulin resistance and high insulin levels) I could gain weight just by looking at food it seemed.

I think everyone is a little different in this respect. When I started losing weight it just melted off till my body reached about a 22 BMI and did not stop much along the way. My wife on the other hand lost about 2/3 of what she needed then stalled out and the last third has been stubborn. So people may react a little differently but I believe the way I explained it is kind of the basics of how it works in general.

John

Edit: when I made the link to Dr Bikman above I noticed he has a new interview video out I had not watched. Going to watch it now. For diabetics (or anyone insulin resistant ie overweight for that matter), they need to watch and listen to whatever Dr Bikman has to say as he is a leader in field of insulin resistance research.

Here is the interview: https://www.youtube.com/watch?v=4fO8MpU_vsc  Anyone concerned with breast cancer needs to watch.