There is nothing free in Germany. I see every month ~800€ leaving my account. It’s on par to Swiss one and as I heard not far from the one in USA. And it’s not good!!! This free health care pays only for basic and/or old treatments.
With what income, which insurance and what type of issue? German public healthcare is pretty comprehensive and cheap (one of the few things I miss) and definitely not on par in terms of price with Switzerland which is even further away from the US nightmare
Nice that you call 800€/month cheap. You are probably seriously rich.
Public health insurance cost is ~proportional to income up to a cap of about 800€ per month. So GP is reaching the cap, for which, by the way, you don't need to be seriously rich. It's IIRC 80k€ or so before taxes per year.