The horrific notion of criminalizing a consensual economic intercourse between two adults -- with prison penalties, at that -- isn't an issue of democratic politics, but of basic rights.
Addressing a problem by going to the opposite extreme is just foolish. There's a reason that most people wouldn't feel safe accepting a ride from a random stranger, and why children are taught not to do it from an early age. Hint: it's not fear of capitalism.
Let's use another regulated field as an analogy: medicine. You have to receive extensive training and receive government certification in order to become a doctor. This is to protect your future patients against someone who knows nothing about medicine, which we can all agree is fair. Here's the difference between being a cab driver and a doctor: if you are qualified to be a doctor, you can be a doctor. But to be a cab driver, you have to buy an arbitrary license from the government of which there are only a finite number of. You could be the safest most wonderful driver in the world, but without that arbitrary piece of metal bolted to your car, it's illegal for you to drive anyone around.
Medallions are not about safety. They are a government subsidy for cab drivers.
But ... the limit is sane. And a retired doctor can come back to work if they see a big shortage (which gives the system time to train more grads).
But that is not the idea of taxi "licensing" as it exists. It doesn't merely regulate taxi driving; it prohibits it altogether, outside of a protected group. It's not licensing, but cartel enforcement. Its aim isn't protecting the safety of the public, but protecting the business monopoly of the taxi industry.
Uber isn't prohibited from operating taxis because they're unsafe, uninsured, or unwilling to subject themselves to registration, inspection, insurance, background checks, or whatever "public safety" requires. They're banned simply because they are competition. And this has nothing to do with public safety!
Was that intended to be a double-entendre?