Do you think anyone at the Bürgeramt has any reason to change their easy "just type stuff and press buttons" job to anything resembling real work? Bureaucrats wield political power, at the very least because they vote like anyone else, but they also have more direct influence than average people. Politicians have no incentive to go against them and, as long as they promise that everything will remain the same, they will have the support of the paper-stamper class. The bureaucrats form a distinct social class with their own interests.
If there was any will to solve the problem, it would have been done already, even without technology. Most people think that taxes are levied to pay for services, but it is actually the other way around, bureaucracy is there to justify the taxes.
[1] I had to go to Lichtemberg because it is was the only office with an appointment in a reasonable time frame.
[2] There are people selling registrations now.
You must involve your landlord because you need some proof that you live where you are registering.
Sometimes the simplest explanation is the most likely: that the system is a disorganised mess, and that those most affected by it (including bureaucrats) are incapable of fixing it.
Yes, there are also people selling immigration office appointments. If there is desperation, there is a business.