I assume that you are german? I have experienced similar here with dermatologists but for allergies. I went to 4 different allergists over a 8 month period to simply get tested to be able to get an epipen which could potentially save my life. This in the US took one next day visit with a doctor. Later (in the US) I saw specialists that put a lot of research into my allergies and time and attention into it. I got nothing here in Germany.
As mentioned before, despite this, I would rather support the german system though. It has its problems like everywhere, but it is at least available to everyone at more affordable prices.
I have often wondered about the private insurance (not that I can afford it). I’ve only been on AOK I can only assume that the care is much much better with private insurance?