Science has proven that cats cannot survive without meat. Unlike dogs that are considered omnivores, cats are carnivores, meaning that most of the food they eat should be meat. By withholding meat from a cat's diet, the cat can quickly become ill. Like lions and tigers, house cats need a diet consisting of mainly meat in some form. To keep a cat healthy and in top form, he should be fed a diet consisting of meat and bone.
Cats need vitamins and minerals too. I highly doubt they can get all the nutrients they need just from meat. Until someone does a peer reviewed study that proves I'm wrong I will likely continue to assume that cats need to eat some type of vegetables or grains every day.
Animals need nutrition just like humans. I don't think an all meat diet can be as healthy for a cat as a well balanced diet. Would an all meat diet be healthy for a human? I think cats need to ensure they get the appropriate nutrition from other foods. All meat won't do it.
Just because something would happen 'in nature' does not mean it is necessarily the best method for managing the diet or habits of a modern cat. House cats are not living as their feral, meat eating ancestors did. Generally speaking they are much safer and more sedentary, so mixing in a balanced diet to meet that lifestyle is not bad.