A similar system to medallions is in place in Australia. Here they just call it "plates".
Anyway, there is a limited quota and they have become freakishly expensive. As a result taxi operators have had to raise their fare accordingly. There seems to be no downward pressure on prices which is bad for consumers.
It's interesting that Uber are challenging this but they seem not to care if they break the law, and I feel bad for the plate/medallion holders who are having their government regulated investment eroded. It's a shitty situation for a lot of people.