That's not a "Black Cab" which would be the equivalent of NYC yellow taxis. A private taxi cannot be hailed on the street, I assume much like yellow taxis. This was once a major advantage, but uber (and equivalent apps) make it almost irrelevant.
Becoming a Black Cab driver is much harder than renting a medallion, though. You have to pass "The Knowledge" which is considered at least as hard as passing a university degree. You have to have an encyclopaedic knowledge of London roads, and generally spend at least a couple of years (often longer) driving around those roads on a scooter so you can demonstrate that knowledge in a series of tests.
I'm not sure if the problem is similar in other major cities, but I expect there is some form of cartel in force in most of the major cities.
However, even if there isn't, there is still a real advantage to profitability from something like uber: if there are enough customers using a passenger exchange, then the likelihood of having passengers near to you is significantly higher. So less of your time is spent in unbillable transit to your next customer. In London there are hundreds of taxi firms; each of them gets some share of the passengers calling them up, so they have to take what they can get. With a central exchange, they get the passengers most suitably located for them from all possible passengers.