In cognitive-behavior therapy with anxiety disorders, I would argue that a strong therapeutic alliance is absolutely necessary but not sufficient. I regularly see patients who have previously been in other types of therapies where they formed a strong, positive relationship with the therapist. They having had a good therapy experience, feel that they got a lot of support, and made some significant personal gains. However, they often report that they still experience the specific anxiety symptoms which brought them into therapy. I do believe that many people with anxiety disorders need more than a good therapeutic relationship to achieve their goals (which might include focused education in the nature of anxiety and panic, training in specific coping skills, a structured step-by-step program of exposure, focused cognitive restructuring to build acceptance of anxiety symptoms, etc.)
Much of the literature on cognitive-behavioral approaches, however, makes it sound like the therapist can just march into the office, throw a bunch of educational materials at the patient, tell them what to do between sessions and that is that. If this were all that was necessary, any good self-help book would suffice. Especially with anxiety disorders, the treatment often involves asking the patient to do specific things which are extremely difficult (approaching a feared situation for phobias, accepting certain panic symptoms and going on with activities anyway for panic disorder, exposure to upsetting stimuli without engaging in rituals for OCD, etc.) Without a relationship of trust and collaboration between therapist and patient, the chances of the patient actually following through are very small.