Medallion owners bought the medallions with the understanding that they were buying into a limited monopoly.
Maybe it should be clarified here that when you see someone claim that it's not the government charging $200,000 for a taxi medallion, that's just the going price on the secondary market. You know, good old capitalism, where people are bidding up the price of a necessarily limited commodity.
The taxi authority looks at population, traffic flow and transportation needs and comes up with a number of taxis that they think should be on the street. Every year, they add new medallions into the system, usually with a lottery. The idea is not so much to protect the cab drivers (cities don't care about cab drivers. If they did, they wouldn't make the minor traffic fines, like your cab being 10 inches over the line of a designated taxi waiting zone, as much as $500 (which practically wipes out the cab driver's week), but to keep the number of taxis from getting so crazy that you have cabs clogging up city centers, fighting for fares.
Another think medallions are used for is to ensure that someone in an underserved part of the city can get a cab. In my city, certain medallions are required for certain times to initiate or terminate a certain percentage of fares in certain parts of the city.