You want a therapist who works successfully with your presenting problem and who is also likely to be able to work with whatever else turns up. Psychological and life problems come in all combinations, which is why the more experienced therapists can cover a wider range. I started off my private practice specializing in depression, childhood trauma, and adult children of alcoholics issues. Problems that look similar can have very different causes and underlying dynamics. Someone who can only do one thing is usually working by formula at a superficial level.
Few people fit a formula.
However if, as sometimes happens with psychiatrists, the practitioner is a competent psychotherapist and then chooses a specialty, that is fine, and should be better for rare problems that generalists might not be adequately prepared for. These are overlapping categories. The term psychotherapy includes counselling about emotional and human relations problems. It also includes work with the unconscious, which falls outside the scope of counselling. If it is working, fine.