And Germany is one of the countries with relatively good public coverage.
I am in the UK, we don't get medicine for some things because it is too expensive: HRT has been in shortage for years, we don't get most newer cancer drugs (it is unrelated to efficacy, it is just too expensive to treat people), epilepsy drugs are the same. Because drug prices here are so low, pharmacies get drugs, and then ship them to Europe to flip. I have relatives who are sick and don't get treated because it is NHS policy not to treat conditions properly (the most well-known one is CFS, the UK's approach to CFS/ME is...unique, and governed heavily by cost). And ofc, lots of money thrown into "cheaper interventions" like public health advertising (coincidentally, the people who run these campaigns are friends with people in the NHS...which is nice for them). Mental health is another area: too expensive, massive underinvestment, even today most of the mental health system is nurses who get a couple of weeks training from psychologists, psychologists are too expensive (somehow, almost no-one who studies psychology in the UK ends up doing clinical work).
There is no trade-off. Someone has to pay because doctors don't work for free. The US has a relatively optimal system with targeted universal healthcare that is heavily subsidised by the wealthy. Germany is a derivative of that system with a relatively large private component that subsidises the rest of the system. It is far better to overproduce healthcare for the wealthy, then underproduce it for everyone else. Ofc, "free healthcare" sounds very nice (unless doctors start working for free, the cost of a US public health system would largely be what it is already...Medicare and Medicaid is cheaper...but not by much because doctor and nurses, for one, are relatively well paid...in the UK, nurses make the equivalent of $25k, again no trade-offs).