That diet would be low in everything except protein. Of course, in theory, that would be better for weight loss. But the question is whether or not that is really sustainable, which is especially important for a long term goal.
IIRC, although your body can run on just the glucose it gets by breaking down fat, it is less efficient. In my own experience this shows up as a negative effect on mood -- which makes me more likely to want to eat (and binge).
