As you know there are no ideal method suitable for every situation and any type of learner. Every method,including Communicative langauge teaching,doesn't always allow to achieve the best results. Although this approach might have many advantages and strong points,it's not always applicable because of students' individual characteristics,their aims and experience.
For example, watch the video Susan Cain The Power of Introverts
It turns out that introverts (who are intrapersonal learners) don't necessarily enjoy group or pair work which is one of the main forms in modern language learning. Their solitude is a prerequsite of effective and creative work.