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 __un__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.
There you go, I fixed that for you.
If the regulators approach to the problem described was the correct one then why can't I get a fucking cab when I want one? There are many more solutions to the problem of oversupply that you identify, indeed one can quite happily argue that Uber actually have one.