I had to ask about 5 people "wait, so I REALLY don't have to file taxes?? Seriously?" after I moved to Ireland before it really sank in. The answer is no, and if you need to change your tax situation (for instance, if you get married) a simple email to your local PAYE office will often suffice. I email DubNorthCityPAYE@revenue.ie and usually get a response within a few days.
Of course, the sad thing is that I actually DO still have to file taxes. To the US.
I'm a PhD student, so of course your mileage may vary, but at the end of the year I have two options: I can accept that whatever the government deducted from my salary was correct (and do nothing else), or I can fill a form if I think I should be getting money in return.
I know that the special cases (foreign income, family outside the country and so on) are a bit more complex, though.
The story is that you can usually get money back by filing your taxes. To file your taxes, you buy this year's software, and block off a straight weekend to enter the data. Or you pay an accountant, who will as likely as not royally bodge it, potentially illegally.
Oh boy, you have clearly never encountered the German bureaucracy. I know it was meant as a joke, but it won't be so funny once you get in the habit of carrying a document folder with you with all the documentation you have for every bureaucracy encounter. The one redeeming quality is that everything is always properly done.
Germany as a collective may seem efficient. Germany on an individual basis is... well, a whole lot of work I never considered before moving here. Good luck to you.
Also, there kinda isn't one Germany. Mittelstand vs Megacorp and different cities are all very different.
German taxes, on the other hand...