The supply of taxis is regulated in the cities, amongst other things, so that the pricing reflects society's ideas of the minimum fair compensation for that class of work.
The constraint on the supply of taxis has no effect on prices, which are regulated separately.
The real effect of the supply regulation is to force drivers to pay up to a hundred dollars per day to be allow to work by some medallion-owning companies and investors.
Lease drivers rent the medallions, and usually the taxis, for a day or a week from their owners or a middleman. Depending on the owner and the night of the week, a lease driver pays $72 to $100 to take a car out for a 12-hour shift, or about $450 to $650 for a weekly lease. The driver must also pay for gas, at $15 to $20 a night. Drivers keep whatever fares and tips they collect, but they often start a day's work $100 or more behind.
Taxi drivers already were consider contractors and didn't have benefits, so I'd really like to hear that argument.