I wonder if it is only the low carbs in isolation that work. I assume the higher protein content is more important to neurological function than fats. The fats have already been shown to be beneficial to insulin tolerance.
It’s been years since I’ve read much on this diet, but IIRC it’s not just eating a lot of high-fat foods and staying away from carbs; it’s a fairly strict diet that has to be followed very carefully. It can work amazingly well but it does require commitment.