Another thing that isn't much discussed in medias, is that a few companies, most notably G7, own most medallions and lease them to (poor) drivers, often together with the car and the radio reservation service. Those companies typically have received those medallions for free from the state, decades ago, before reselling them became legalized. Those companies obviously pull some strings, both stirring up drivers and talking in minister cabinets.
Anyway eventually they're fucked, Uber or no Uber: autonomous cars will make taxis obsolete at warping speed. Taxi drivers are fucked that much harder than Uber's, because they'll be left with a worthless medallion and its 20 years mortgage. (It's also likely to make private car ownership marginal, something akin to owning your own horse in the XXth century, thus hitting car manufacturing pretty badly once enough autonomous cars have been produced, but that's another quagmire).