A use case diagram provides a gestalt view of the system, showing not just the parts of the system, but also gives a feel for how the parts might interact. It is also useful for new team members coming onto a project, and convincing stakeholders who have problems with written documents but like pictures. More importantly, the process of drawing and staring at a diagram can help you get to grips with the model in its entirety, to find missing or duplicate use cases, missing actors, and so on. Large organisations with formal development processes or ISO certification typically require sign-offs and these diagrams can prove convincing here.
However: Models are never really complete, so drawing diagrams may again give a false sense of security. Drawing pretty diagrams can become an end in themselves, rather than a tool for assisting modelling, especially if you are proud of your prowess with a CASE tool.