Calories get you fat. It's CICO. Protein is satiating, which is a major advantage if weight-loss is a goal. But then again, so is fiber. Many people have successfully lost weight on a high fiber diet.
Losing weight and losing fat is not always the same, a diet with insufficient protein intake might cause muscle loss and thus, decrease metabolic rate(muscle metabolism rate is less than people think, but over a year, it makes a big difference).
However, i understand that not everyone cares about preserving muscle on a diet, some people just want to be slimmer, fair enough.
Well there's no reason it has to be "insufficient" and having too little protein is certainly a bad idea. If you consume a source of protein at every meal, whatever the makeup, you can easily hit 16%+ as part of your macros. Even vegetables like broccoli and peas have protein.