I think we already know that "low-carb and high-protein" doesn't work. You also need high (or moderate) fat. Low-fat protein is also highly insulogenic. High insulogenic foods = insulin resistance which leads to obesity, metabolic syndrom, diabetes, and likely Alzheimer, heart disease, and so on.

The higher the amount of fat taken with protein, the less insulogenic the food is. Also, it seems Vitamin K2 exists almost exclusively in saturated fat, and Vitamin K2 is what protects you from atherosclerosis, osteoporosis, and heart attacks, too. There are many other vitamins and minerals stored in fat, too, possibly because fat is the body's "reserves" which means more just than "high-density calories".

After all, the body needs vitamins and minerals, too, to survive. And if it can't get them while not eating, then it makes sense that they should be stored somewhere (they are stored in the liver, too, but the liver is more of a short/medium term storage).

However, you also have to keep in mind that fat stores toxins, and in our high-pollution modern world, it may not be a good idea to eat too much fat, or at least you should be watch out where you're getting your food from.