All discussion aside, I see portrait photography as painting with people.
That is, it's not so much about composition, as it is about using objects around you - people, nature, etc - to paint a picture instead of using paint and brushes.
It's much easier than painting when the picture you see in your head is much like what the camera lens sees when you point it in a given direction.
However, often there's work required to paint the picture you see in your head. With people, it's figuring out what to say to them to make them look the way you see them - to bring out the inner warmth - and to figure out how to capture in a static image what the eye sees over a stretch of time.
Ultimately, with movies we've come full circle: filmmakers often resort to painting (i.e. CGI) instead of photography, because sometimes it's easier just to paint the picture one has in their minds with a graphics tablet than it is to paint it with real-world objects positioned around the camera - even if realism is the goal.