I had a small therapy only practice for a while but I didn't like seeing other psychiatrists doing crazy things with my patients' meds and slowly came to embrace prescribing. In private practice, you can do whatever you like. If you want to have a practice that does not prescribe meds then you can do that. I will tell you that Americans have come to so wholly embrace meds even therapists recommend meds to their patients. There was once a time when psychiatrists rarely prescribed meds and many were hostile towards doing so. My former chair from residency once recalled being berated by a supervisor as a resident for prescribing an antidepressant ("what your patient needed was an interpretation, not a medication!") Now we've swung the other way with very few psychiatrists doing therapy and a whole generation (sometimes called the lost generation) of psychiatrists who trained in the 90s graduating with little to no therapy training at all.
Psychiatrists have come to be so defined by our prescription pads in the mental health arena, that we are often devalued as "prescribers". Your value is in part based on your medical training and ability to prescribe. If you want to forgo prescribing meds, expect to take a hit to your income unless you're a phenomenal therapist and marketing genius.
Of course, there is nothing stopping you focusing on another modality such as psychoanalysis, CBT, ACT, MBT, DBT, mindfulness, group therapy, couples therapy, family therapy, schema therapy, EMDR, IFS etc
I do sometimes still do split treatment where I am the therapist and another psychiatrist is the psychopharmacologist. This model could be beneficial when dealing with certain patients (e.g. personality disorders, trauma, somatization).
