I think you're dramatically oversimplifying things by saying that the pilot is just keeping an eye on the autopilot. There is a lot more going on in the cockpit in these situations than simply programming the autopilot. They're running checklists, troubleshooting, navigating, briefing the approach, communicating with the flight attendants, potentially also briefing passengers, potentially briefing their company/ops folks, etc. There's a lot to manage in these situations.
Similarly, the controllers aren't just managing the traffic in their area. They're also coordinating with their management, other controllers that are managing neighboring sectors, emergency management folks, etc.