Two foundational tenets of Lean is leadership and systems thinking. Both relate to the fundamental philosophy that systems affect people significantly and that it is management’s responsibility to create the environment within which teams can work autonomously towards the goals of the company.
Scrum Masters somewhat already have a limited aspect of this role in that they are responsible for removing impediments to the team. This relates more to how the team interacts with those outside the team. But within the team, Agile team coaches also have the role of facilitating improvement of the system within which the team works.
While teams need to self-organize it often doesn’t happen spontaneously. Many developers got into software so they could work alone. Creating a true team often takes someone’s energy. The best way to do this is to make it easier for people to work as a team than to work by themselves. One learns and gains trust and respect better by working together than by talking about it.
An Agile team coach doesn’t make decisions for the team, but should be an energizing factor in how the team comes together and be providing new ideas that will make them more effective.
You can get more tips at our Tips for Agility page.