This is a great question. Strictly speaking, there is no single Mediterranean diet, since every country in and around the Mediterranean has different foods.
The āMediterranean dietā is a construct by Walter Willet of Harvard, and while it is healthier than the standard American diet, it is still quite high in carbohydrate and is relatively low in protein. Dr. Willet is a vegetarian, so the Mediterranean doesnāt encourage the eating of much meat, especially red meat. My impression is that, while it is not a low-carbohydrate diet, it does encourage the eating of whole foods and the avoidance of processed foods, which is in its favour.
There is a write-up of how the Mediterranean diet was formulated and introduced in Nina Teicholzās book, The Big Fat Surprise.
Also, because Dr. Willet has a lot of influence at the U.S. Department of Agriculture, it is one of the dietary patterns recommended in the current U.S. dietary guidelines, which is administered by the USDA. The ketogenic diet is decidedly not recommended by the USDA, and Dr. Willet is strongly opposed to it, as well.
Bear in mind that the United States is a major producer of soybeans and maize (corn), and hence a major producer of soybean oil, corn oil, and high-fructose corn syrup. Part of the mandate of the USDA is to promote the sale of American agricultural products, which is a strong pressure keeping the emphasis on eating grains in the U.S. dietary guidelines.