I've been living in Germany for more than 7 years and I can only verify this. The offices in big cities are overloaded with requests and getting an appointment for things like renewing documents can takes weeks if not months. Not to mention the naturalization process which can take up to two years[0].

A solution for this in my opinion would be to centralize these processes and make them online, like making a government portal for the whole country. But for that many rules should be changed, which is highly unlikely.

[0] https://www.tagesspiegel.de/berlin/zwei-jahre-warten-auf-die... (German)