>No, the work of the manager is to do whatever is needed to deliver the result on the task assigned to them
You missed the part where the manager has to evaluate and push back if needed. If their primary role is merely to do what their bosses tell them to, then they are not doing any managing.
99% of the companies can replace 75% of the managers with supervisors ( foreman in constructions/manufacturing ) and get a better result. Most of the "teams" inside organizations dont need managers - they need supervisors as organization does not need to have mini fiefdoms.
You missed the part where the manager has to evaluate and push back if needed. If their primary role is merely to do what their bosses tell them to, then they are not doing any managing.