What does the Incident Commander do that the other incident roles deliberately do not?

Why this is the answer

The commander’s value is altitude: they keep the whole response in view, assign roles and decide, which is only possible if they stay out of a terminal themselves. Applying mitigations is the operations lead’s work, and a commander who does it loses the overview. Outward updates belong to the communications lead, who shields the responders from that traffic. Keeping the timeline is planning work. Each is a separate role precisely so no one person carries all four.