I think that the word "cured" is being used as many of the type 2 diabetes patients did not need any medication any longer. Not needing medication means that you are cured, is the line of thinking. That is what the colourful bar chart in the quoted study shows.
There are many people who disagree with you on this one. They claim that they feel much more alert and awake when they live on a low-carb-high-fat diet (e.g. keto diet). Carbs make them feel drowsy, sleepy and less alert.
Cured to me would be having someone drink 100 g of glucose and not spike to 250. Then they would be back to normal in 2 to 3 hours. ----Controlling A1c and improving to me is not the same thing as being cured. ---I agree that all that is listed in Baron's opening posting is very good. It's just the word "cured" or "cure" that I question when discussing this subject.
Ketones definitely can fuel the brain but we'll have to agree to disagree on how well. I do agree that there are no essential carbohydrates.
Well, at least the bread I usually eat has a meaningfully lower GI, and is probably more filling than table sugar.