Bürgerämter are most of the time a fucking joke. My registration in Berlin took months after I already moved there, the waiting times are just that long, and this seems to apply to many cities. I live in another city now, and my ID card has been expired for months now (which, legally, is a misdemeanor). There isn't a single free appointment anywhere, citywide. You can attempt to go personally there in the early morning, yet here is what I encountered: arriving half an hour early to the Bürgeramt: THIRTY people waiting there, squatting in the hallways, all the way out to the door. On another day, arriving an HOUR before it opened: 12 people already waiting. It's all a joke. And this isn't a recent phenomenon - it's mismanagement for decades, the people responsible should all be fired (but of course that isn't possible).
There should be a "Minister for Time", who has the authority to crack down on such bullshit, not only in the German state bureaucracy, but also in the medical system (good luck getting any quick care here!). Both have taken to a level that is undignified, and wastes person-years of sitting in depressing places. Waiting should be an exception, not the norm, and there need to be metrics against that which have consequences.
I also wrote something similar for getting a NIE appointment (foreigner's ID card) by using puppeteer (headless Chrome for node) to actually fill out the website for me, about once per 3 minutes (max without getting rate-limited).
I'm fortunate to have the skills to do so but I feel bad for the rest of the people who have to check websites for weeks at a time to get appointments.