I try not to overbook at my office. I have about 16 slots every morning for returning patients (fewer if I have new patients booked, which I usually do). I usually schedule, counting new and old patients, 12 patients every morning. If I were to cut my appointment slots down to 10 minutes instead of 15, I could really pack 'em in, and I may have to do that some day, but with the 15 minute slots, I can usually squeeze in people who want to walk in because they're sick. There's only so much that can be done to control the flow; if someone has chest pain, I'm going to be running late from then on. If everyone is well, I'll be right on time.
Influenza is the destroyer of schedules. If I have 12 slots booked, and just two people with the flu want to be seen, I'm either going to squeeze them into the middle of the schedule or tack them onto the end. Either way, I'm going to run late, and patients will feel it.
Imagine a similar phenomenon nation-wide. Primary care physicians are trying to see their new patients, physicals, blood pressure and diabetes follow ups, and everything else, and for a few months, several more patients per day need to be seen. This is what happens during a bad flu season. Wait times will go up for both the flu patients, and the diabetics, and in a short period of time, appointments will be unavailable anywhere.
Now think bigger. Think of a large hospital with, say, 100 ventilators, with usual staffing for 80 of them. While most people with the flu don't get terribly ill, some do, and may need mechanical ventilation and ICU care. Some of those out with the flu may be nurses, respiratory techs, and doctors, but if all of them stay healthy, and the hospital can find extra staff for all 100 ICU/ventilator beds, what happens to respiratory failure patient 101?
Here's some reading for you.