How would knowhow of anatomy benefit a songster?

it would allow him/her to control breathing better?
By understanding the use of resonance produced through the throat, loud cords and mouth. The better the resonance, the better the sound ability.
Knowledge of anatomy would be of value to a singer because of the physical dynamic of singing. Some positions would prevent the vocal chords from working properly. For example, sing the lowest write down you can hit with your chin down, after try to hit it with your chin up-----see what I parsimonious? Knowledge of how the diaphragm works to propel air from the lungs would be another. There are miriad reason why anatomical knowledge would be advisable to a vocalist. Now, for your lesser question-------Another occupation that would benefit from knowledge of anatomy? Well, how more or less a Doctor or a Surgeon, or a mortician, or a physical therapist, or a tailor, or an artist, a masseuse, an anatomy tutor, a fashion designer, etc, etc.
Hope this help answer your question!