> What other better solution do you imagine?

I believe there are two ways to deal with a system that's not working as intended.

One alternative is to have shock buffers for unexpected circumstances. Berlin, known for its chaotic nature, used to have a second queue at the Foreigner's Office for people who needed an appointment today. You had to queue sometimes even from 3am on, which sucks, but it sucked less than having to cancel your holidays because you couldn't get an appointment. In my case all I needed was a signed piece of paper saying "this person is allowed to stay in Germany until we finally process their papers", but the office had no mechanism (or no will?) to do so.

The other alternative is to pretend that the system works fine, which is what the German administration is currently doing. Sure, I could hire an attorney to sue the government - it will cost me an upright investment of 1k€, it will take months, and all I'll get afterwards is most of my administrative costs (forget about my canceled flight) and an appointment.

Edit: on the topic of the GmbH, it is a complex topic because the German government made it complex. Estonia, Texas, and my own home country have much simpler rules for starting your own small company. Every government keeps promising "we'll simplify bureaucracy and we'll digitize" and yet all we get is new rules and more letters.