The problem is that if you have a single client, the government may claim that you are trying to avoid tax and other obligations --- that you have a fake company.
Couldn't I just pay all of that stuff by my own to show them I have no intention to do so? I want everything to be legal. I do not want to save any money in taxes, health insurance or social insurance. I am actually happy to pay all this. Nevertheless I heard horror stories even by doing so you are at risk they will f..k you anyway after a Prüfung (audit) within the first five years or so.
Wouldn't you actually be paying more taxes as a one person company? Why does it matter if the company has only one client and one employee if everything is paid properly?
Because as managing director you don’t have to pay pension insurance (and others). So if you are employed, the social system will get more contributions.