- to keep traffic down
- to ensure a minimum standard of vehicle
- to ensure safe, well-trained and responsible taxi drivers.
- to ensure a fair level of income
- etc.
However the main problem with the medallion system is that they can be traded, speculated on, and used to extract "rent" from workers further down the chain. This benefits nobody.
Surely there could be a happy middle way between the libertarian nightmare, banned-in-half-of-Europe Uber model; and the old-skool union cartel medallion model.