Psychiatrists oversee treatment and give medication. They don’t do psychotherapy, so they are not in the business of offering EMDR. Easily confused but very distinct jobs.
Many psychiatrists only prescribe, some also do psychotherapy, and of those, some do EMDR. This is less common today than it used to be due to insurance and time and how they get paid, but some of those in private practice or academic settings still provide physiotherapy.
Sorry, I should a put a source: partner is a therapist.
Edit: autocorrect changed psychotherapy to physiotherapy.