Respectfully, you'd be studying the wrong thing i.e. the "system" without the system-keepers. Study the organizational structure; then study the people working within that structure with their aspirations and incentives; then go back and rejig the system; but, don't forget to put the stick figures on the diagram too i.e. users and makers.
Yes, that's an important part of any system. It sounds like we agree that the traditional diagram, with some boxes and some arrows between boxes, is quite inadequate when you actually have a tough problem that needs solving.