So, for example, if a uber driver has an accident, he has to pay himself for all the costs.
This ruling also provides safety for the drivers, because the driver (which has to behave as if he was an employee) now also gets the protections valid for employees.
Can't the employee get an insurance by himself?
At that point, the employee has the disadvantages of being an employee, and the disadvantages of being a contractor, but the advantages of neither.
There are quite some major differences from being regularly employed. For example, you can work whenever you want including never. Let me know what your boss says about that.
A lot of regular employments have this, too. Even employees in some government agencies in Germany can just decide to go to work 3 hours later, or not at all that day.
This is not something that is specific to contractual work.