Could people be trained to change personality traits?

One way of treating a phobia is through desensitization. If a person has a fear of spiders, for example, the person might first be taught to relax while looking at a photo of a spider and be led through a process of exposure and desensitization to closer and closer approximations to actual spiders.

Phobias are fairly non-complex behavior. Consider now more complex changes that a person might want – assertiveness, anger reduction, greater compassion, conversational skills and so on. Assuming that money is no object in the treatment, suppose that a therapist used trained actors to simulate various types of social situations that would require in gradually increasing amounts the exercise of the desired personality trait. Do you think this might work? To what extent are our personality traits habits that we have gotten into?