You can get the same effect with much less lifestyle disruption just by exercising. Specifically low intensity cardio trains your body to metabolize fat efficiently.
It doesn't. That's why "Hungerast", i.e. sudden loose of energy due to all carbohydrates being used up is a thing in all endurance focused sports.
It's actually not a thing in "all" endurance sports. Once you push into the realm of ultra endurance, athlete become so efficient at fat metabolism that they never "hit the wall" so to speak.
What does metabolizing fat have to do with carbs giving you brain fog?
The brain fog is caused by rapid fluctuations of blood sugar. Low intensity aerobic exercise has a number of positive effects that all play off each other: You metabolize fat more readily as an energy source, which makes your body less reliant on carbs. This alleviates the exhaustion you might normally feel as your blood sugar crashes. And carbs (and especially refined sugars) are routed directly to muscles, blunting the insulin response and increasing insulin sensitivity.