> You need to get private healthcare

No you don't, you can stay in the public system.

> you need to save up for retirement and so on

You can still contribute voluntarily to the public pension if you want to but the majority of self-employed people here don't as this is seen as a feature not a bug.

Part of the concept of being self-employed in Germany is that you're opting out of the welfare state and are responsible for taking care of yourself. With the potential upside of better raw earning potential.