"Having mainstream appeal" does not mean legitimacy as a scientific discipline. Psychoanalysis is about as useful as alcoholic anonymous' 12 step program: it's a terrific placebo. Mainstream theories are largely discredited by neuroscience and psychiatry, but it turns out having people just sit on a couch and self-reflect is usually beneficial regardless. But if you want to understand the how's and why's of the human mind with scientific rigor, then do not look to anything in the field of psychoanalysis.
Very few people use psychoanalysis as if it were scientific, even its practitioners. There are also arguments that with some effort in the field it could graduate to science. In general, though, the Popperian criteria for science are not the end of knowledge.
