"please enlighten me how requiring to pass a test that you fit to transport others"
What is a person going to do as an Uber driver that would hurt others that he couldn't do just driving himself or his friends around? If there is a danger posed by an Uber driver, then the same danger is posed by regular drivers, and EVERYONE should be subjected to the same tests. Don't punish people for carrying out commerce. That is oppressive and hurts the people.
"requiring more frequent car inspections (since the cars are also used much more intensely)"
The cars are also owned by the drivers, who will notice when something is wrong, and get it addressed quickly, since they have to pay for it and don't want damage to compound. If the car is unsafe, the passenger will notice, give a bad rating, and complain to Uber, who will quickly deactivate the driver contengent on getting his car fixed. This is called market regulation, and it is 1000x as effective as corrupt government regulation. All you have to do is find a corrupt inspector and slip him five extra bucks and your car will pass ANY inspection.
"or an insurance that covers potential damage you your customers is oppressive and illegitimate?"
Uber already provides that, though there is a meme going around that they don't. It says they do right on their webpage. $1 million in commercial insurance, just like a regular cab.
"Good luck in your anarchy, which will end up in despotism after a while."
Freedom is like food for the people. Oppression is like starvation. You have to eat every now and then to live. Complaining about having to eat because you will just get hungry again later is not a legitimate complaint.