Is there a difference between free association speaking vs free association writing? Is psychotherapy more effective when examining free association speech?
Free association is an integral part of depth psychological therapy (such as psychoanalysis), which is still prevalent around the world (e.g. in Germany depth psychological therapy and cognitive behavioral therapy are the only two therapies paid for by health insurance).
The problem with writing would be that it slows down the interactive process between therapist and client. It has been suggested and there is anecdotal evidence that outside of a therapy, free association writing can be a useful tool for self-knowledge. Within a therapy free association is only one part of the methods and its usefulness is dependent on other processes such as transference and countertransference, which need the presence of a therapist.
To my knowledge, there have been no attempts at purely written (e.g. online) depth psychological psychotherapy. I believe such an impersonal setting and slowed down communication would hinder the interpersonal processes and actually the spontaneous workings of the subconscious needed for depth psychological psychotherapy to work.