People who want accent modification training sometimes choose to go to speech therapists because they may be covered under their medical plan. Speech therapy is a medical profession and they work with abnormal issues in speech. Because they understand the mechanics of speech, some have started tapping into the business of accent modification since there is a great need, much greater than for regular speech therapy.
The drawbacks of working with most speech therapists are: they are generally not trained in the English language, culture or teaching, and they often charge a higher rate per hour.
A speech therapist is in no way better than an ESL teacher who has studied accent modification training and culturally appropriate communication. (Both of these areas are Voice to Word’s specialties.) In fact, there are additional benefits of working with someone experienced in language teaching since many times the issues of clarity include aspects other than accent, for example, volume and projection (which can be culturally influenced,) ways of expressing oneself (which can also be culturally shaped,) as well as tone, grammar and other aspects of stress and intonation which can totally change the intended meaning.
I certainly don’t think an accent is a medical abnormality. We are all influenced by our native language and it is a matter of building awareness and understanding the differences. From there it involves repetition, practice and integration, both at the physical and psychological levels.