Ymmv, I think it mostly depends on where you live, how flexible you are, if you're willing to call another specialist practice when the first is booked and whether you're insistent. And on the specialty, obviously, I'm sure there are some that are perpetually overbooked, which I was fortunate to not need myself so far. There's an artificial limit on the number of medical practices in Germany, as well.
Incidentally, my relatives who live in more rural areas seem to think nothing of driving twenty minutes for every trivial thing sometimes multiple times day, but driving 90 minutes to see a specialist twice a year is totally out of the question.
Nope. I can see my Primary care physician today if I wanted to. It's currently 10:55 AM. If I had called before 9, I would have gotten a scheduled slot. If i wanted to see him now I'd have to go to the open office hour and wait 30-60 minutes.
For urgent (not emergency) stuff, the 4 hospitals in my city have daily open office hours with specialists. Without an appointment, you usually wait 1-2 hours (unless they prioritize you due to pain).
For non-urgent things like a diagnostic MRI "just to check", you'd wait 1-2 weeks for your appointment.
There are two exceptions to this: We got a lack of dermatologists and psychologists and you'd probably wait 2-3 months for an appointment.
Now, unless I really have something wrong with me, the treatment will probably be "take 2 paracetamol and come back in 2 weeks if you don't feel better", but that is a different problem from not getting an appointment at all.