Why is it necessary for controllers to avoid undue delays when handling minimum fuel situations?

In minimum fuel situations, it is crucial for air traffic controllers to avoid undue delays primarily because these situations can escalate into emergency scenarios. When an aircraft indicates it is on minimum fuel, it means that the aircraft may not have enough fuel to handle unexpected delays or diversions, and the safety of the flight can be compromised. Minimizing delays allows the aircraft to land safely and avoid the risk of running out of fuel, which could lead to a potentially dangerous situation for everyone involved, including passengers and crew.

The other options, while relevant to air traffic control operations, do not capture the immediate safety-critical nature of handling minimum fuel situations as effectively. Ensuring traffic flow is important, but the overriding concern in this context is the safety of the aircraft. Prioritizing air ambulance flights pertains to a specific type of urgency rather than the general principle behind handling fuel emergencies. Compliance with standard operating procedures is vital in all air traffic control operations, but it specifically serves to facilitate safe handling of incidents rather than directly addressing the urgency of fuel shortages.