I like the healthcare situation in Germany but normally you would have to wait months for a surgery, if it's not very critical. An appointment with a specialist can also mean waiting weeks or months.
That's not that uncommon in the US either though. My mother had an issue that required seeing a dermatologist, and just getting in to see a dermatologist was initially going to take about 6 months. After calling for a month, she was eventually able to get her wait down to 2.
I don't know where this idea comes from. I'm American but my experience with healthcare in European countries where I've lived (England, France, Czech Republic and Switzerland) is unparalleled. I had my gall bladder removed (non-critical) in France; the wait was two weeks and everything about the experience was impeccable.
Weeks is not bad... Months is. And as you said, it's for non-critical stuff.
A mixed system - government-managed for important things, with extra healthcare you can pay on top, like the one we have here in Uruguay, seems to work best.
As far as I can tell, we have the best healthcare for anything but special/rare cases which would be best served by a top specialist from the US or Germany. For the remaining 99% of cases it beats any system I know of.