As an American living in Berlin, it's a striking feeling to live in a well-run country. It's not perfect of course, but the feeling that the system works with you and for you (even as a foreigner) is a stark contradiction to the US.
living in berlin feels like living in a failed bundesland. the public transport is broken all the time, the bürgerämter are crowded, you can't appointments, the administration is basically clueless, ...
i guess if you don't rely on public services it's not that bad, but still, berlin is a very bad example for a functioning german place.
The biggest surprise to me as an American was that I had this perception that health care is free over here, and it's not. You are mandated to pay your health insurance, which isn't as cheap as you might imagine, but it is of course pretty comprehensive with no co-pays for every service that I've ever had.
Btw, the health care system is a dream of efficiency compared to the US.
The appointment system for the Bürgerämter is a bit of a disaster, but you can go without an appointment, or get appointments further away, which you will have no problem getting to due to the great public transport system.
Have you lived outside of Germany at all?
In Berlin I get home with the underground at night (01:00 - 04:00), last one in Stuttgart comes around 01:00.
In Berlin a 9 minute wait is considered long and in Stuttgart 20 minutes is long.
Almost all people I know, that moved from Stuttgart to Berlin find it horrible to ride by public transport in Stuttgart now.
I spent about a month living in Hamburg, and visited Berlin for a day, and I never had to wait more than a few minutes for a bus or (more often) train. As importantly, they consistently run on time, so I don't need to leave a massive amount of padding if I want to arrive somewhere on time.
I don't know I'm qualified to say whether your public transit is objectively bad, but to me it's subjectively amazing.
FWIW my experience has been that it's surprisingly difficult to compare my 'home', Amsterdam, to Berlin, or The Netherlands to Germany. There's tons of things that I prefer in the latter (cost of education, civil society/engagement), but also plenty of things I prefer in the former (ease of starting a business, relative lack of (monolingual) bureacracy).
But from talking to expats to both Amsterdam and Berlin made me realize that even the shitty parts of my world are much better than where some of them came from. Most of my complaints about Berlin or Amsterdam pale in comparison to the benefits it offers to many people from other places.
(For example, the complaints about DB (Germany) or NS (Holland) are ridiculous in comparison to my experience what almost every other part of the world)