There are also essential fats, ω-3 and ω-6, to be precise. So just as we need some protein each day, in order to get all the essential amino acids, we need to eat some fat, in order to get the essential fatty acids.
Also, it pays to consider where the calories are coming from. Protein stimulates insulin production, albeit at half the rate of carbohydrate, and low insulin is a primary goal of this way of eating. Since fat hardly stimulates insulin production at all (certainly a lot less than carbohydrate and protein do), it is the safe source of energy, if we want to keep insulin low. Hence the recommendation to keep protein moderate and eat fat to satiety.
Note that that is "fat to satiety," not “fat in excess.” Just saying. 