One of the problems posed by desire is that it lies outside the realm of reason, untouched by logic. Any scientific analysis of it, in the Wittgenstein sense of scientific, would be seen by Wittgenstein as misdirected. It would be of no use.
Deleuze and Guattari denounce "a system of allegorical interpretation in which the dates of one narrative line are radically impoverished by their rewriting according to the paradigm of another narrative," Frederick Jameson writes.
Yet the inverse holds as well: While psychoanalysis may be seen as misapplied when brought to bear on literature and other aspects of culture, it's rightful place remains the realm of desire. And if desire is a realm in which reason is subjugated to the passions, to feelings, then science would have no application as an explanation of its content and characteristics.
Wittgenstein, of course, knew this, and admired Freud for inventing a manner of speaking that filled the void of how to deal with desire, a void left by the development of rationalism, begun with Descartes, during the Enlightenment. Wittgenstein's quibble is that Freud thought his method a science when, in Wittgenstein's eyes, it was not.
Wittgenstein Contra Freud: The Myth of Psychoanalysis
Points of Contact and Criticism Between Wittgenstein and Freud
A Wittgensteinian Approach to Discourse Analysis
Indoctrination and Resistance in Psychotherapeutic Dialogue
Construction of The Double As Social Object