I am a speech therapist and a person who stutters. It’s what makes me so passionate about working with people who stutter. There are actually quite a few well known speech therapists who stutter. But yes we could do with more lived experience of stuttering in the profession (I can send you a list if you’re interested). Some of the hosts of the StutterTalk podcast are therapists who stutter for example. Let me know if you want to discuss applying / what the job is like etc. That said, I know many excellent therapists who are very insightful about the psychological side of living with a stutter but who have not stuttered themselves.