So why do we still use psycholanalytic theory?

I came across this article from the New York Times on Freud's place in education:

Freud Is Widely Taught at Universities, Except in the Psychology Department

We talked in class about how Freud and his theories are considered too flawed to be considered within psychology. Are his theories still relevant to literary studies? I feel like we need to know Freud to understand Plath, for instance, since her work was so influenced by his theories. However, I am wondering if it is valid anymore to use Freud to interpret the work of Shakespeare and other pre-Freud works. Should we develop a more relevant psychology-based theory instead?