The CMF is the single best way to monitor your queues in your monitoring system, and most people don't do it. Almost everyone has a graph showing the current queue depth. They might even have alarms on it.
But if you see the queue depth going up, how do you know the cause? There are two possibilities: arrival rate increased quickly, or service rate dropped quickly.
But with a CMF, you can tell just by looking! One of the two sections will be getting fatter, telling you immediately where to look for the problem. If service rate is slowing, then you know to scale up your processing fleet, or look for a pathological case that is blocking processing. If the arrival rate is increasing, you can put in some backoff or load shedding, or just be happy about how busy your product is!