Stuff like that is super-annoying, but I wouldn't drop a doctor I liked over it. You can just as easily get a doctor who's like that too. And there may still be the same administrative problems.

I always used to get my healthcare from a hospital system that tended to have lots of problems like that, but often has really nice doctors. At the ultrasound where my endometrial cancer was recognized, they did something like this, and also couldn't schedule me with a gyn-oncologist right away because the scheduler was out of town. So I went to the other hospital system in town, which is more organized. But my oncologist there is either overworked or is putting in the bare minimum effort to provide me with paint-by-numbers care. And he's a @+#&. (The NPs are nice though).

One of my New Year's resolutions is to get a new, nicer oncologist back at the disorganized hospital.