Your body and your brain can survive and thrive without carbs. You may have not known this but nowhere are carbohydrates listed as an essential nutrient . The reason why carbs are at the center of every standard diet is simply that they provide the body with a cheap and easy source of energy, especially for the brain and muscles.
In the complete absence of carbs, studies show that your body survives with the help of gluconeogenesis and ketogenesis (glycerol and ketones) . But the keto diet does not exclude carbs completely. That means, that you'll be giving your body a minimal amount of carbs to get the best of both worlds (glucose and ketones).