I see so many "why don't they just do X, it would make more sense" arguments about all kinds of government programs. The reason that don't in every case is because from the government's perspective the program is working great! The existing medallion owners very much like being able to charge monopoly prices. The city politicians very much like that the medallion owners lobby them to keep the system in place and support their campaigns. Why would they want to mess with something that works just fine? You are not the government. It doesn't serve your interests. It serves it's own interests.