This situation is not unique to health care. It's a big guy vs little guy thing. The big guy tunes its system to optimize its use of resources. If this is less than optimum for the smaller guy, that's too bad. To some extent it's a "power" thing. Wait on hold is a classic example. The big guy doesn't want to have a second of slack time for the agents, while the caller is trapped in the queue. It's nearly impossible for the caller to manage time while waiting in the queue.

Recently, I had to cancel a health care appointment. Unfortunately, the (completely justified) situation developed outside of their office hours and they did not provide any practical means for me to convey the information in real time. Eventually, hours after the appointment time had passed, they picked up the message, then chastised me for disrupting their schedule by not contacting them.