Scientists make hypotheses, construct experiments, evaluate them statistically, etc.

This seems too narrow a conception of science: Did Darwin do science that way?

What Freud didn't succeed in is to elevate psychology from a preparadigm state (in Thomas Kuhn's sense). But Freud's main concern was mental conflict, and I don't think its study has today reached the stage of genuine science. Cognitive-behavioral approaches to treatment largely ignore mental conflict, and the result is that they are more collection of tricks than a theory. Because students typically set the bar too high for psychoanalysis, Freud's own principal trick, free association, is vastly under-utilized.