Except uber DOESN'T work with the free market. It ignores all of the laws and regulations for consumer protection and safety that other businesses have to follow, like adequate insurance.
Uber drivers do have insurance: they get it automatically from Uber.
(If the driver feels that Uber's insurance policy isn't adequate, because for example there is a high deductible for body damage, then the driver can purchase hybrid commercial-personal policies from the major insurance companies. Then that doesn't really have anything to do with public safety: the passengers were already fully covered by Uber.)
And of course the vehicles are subject to stringent safety inspections and standards (more than taxis are).
And Uber drivers are required to drive to any destination in the area (by law and by the company) do dont try to say that they are discriminating. Uber drivers don't even know what your destination will be, until you get all the way in the car.
And Uber drivers undergo a more stringent background check than taxi drivers in NYC.
I'm no fan of Uber, actually, but I don't see any "consumer protection and safety" issues. When you get into a cab, does the taxi company know exactly who you are, and where you are in real-time on the trip, and separately where the car is, and where you were dropped off? Uber is shitloads safer than a taxi.