Training as a lawyer does not prepare someone to work as a teacher. Training as a lawyer may be helpful if the person is going to teach law.
Training in mental health does not prepare someone to work as a coach. Training in mental health may be helpful because of transferable skills or if the person is going to coach people with mental health issues.
In coaching, the skill of the coach makes a difference. It is also true that the person being coached must be engaged in the process to benefit. On the same note, the content of the training and the methodologies used for delivery impact the value of the training; of equal importance is the attitude and effort of the trainee.
Ultimately, it makes sense for a professional offering coaching services to be appropriately trained. It also makes sense that their training meets a standard. For this reason the International Coach Federation, ICF, approves training programs and requires 60 hours of approved training for members. While membership in the ICF is not a guarantee of skill, it does indicate a vested interest in training standards.