The body still needs carbs.
You'd suffer brain damage with a zero carb diet.
What people need to do without is sugar and processed white flours.
It's virtually impossible to eat a zero-carb diet, even if you wanted to. Carbs are in fruits, vegetables, milk, pretty much anything but meat and fat. But most of the carb-overload we take in comes from sugars, white flours, grains, as you mentioned.
I tried Atkins for about six months about four years ago and really did not lose anything. I was not exercising at the time and I took them at their word that you could eat as much as you wanted as long as you avoided the carbs. I also think I ate too much peanut butter (one of my big weaknesses).
This time around, I'm eating basically chicken, turkey and fish with beef about once a week. Trying to stay way from the really fatty and high-cholesterol stuff. I've cut back but have not eliminated dairy products (milk and yogurt) and I am still eating 2 or 3 servings of fruit a day. What I've eliminated are the starches - potatoes, pasta, rice, bread, grain of any kind). It's still basically a balanced diet. Hopefully the elimination of the starches combined with the exercise regimen I'm on will yield some results this time.