I am always trawling youtube for diet and health videos.
I came across this old one on Atkins and like it.
https://www.youtube.com/watch?v=epxp_Viq484
In short, low carb works because eating lots of protein makes you feel full which means you consume less calories than you normally would.
It's nothing to do with ketosis or the efficiency of turning fats and proteins to energy versus that of carbs or anything to do with this BS we keep hearing about eating lots of fat (which, they find, actually make you eat more food, not less compared to a low fat diet).
It's simply that eating protein, makes you feel fuller, therefore you eat less which means less calories in.
Based on my diet experience (which is not Atkins) it makes sense.