How so? I'd say it's opposite. Today when you pay a taxi ride you're not only paying the driver and the maintenance of his cab, you're also remunerating the capital the medallion's owner. If medallions were not tradeable, you wouldn't have to pay for them.
The market price of a ride is based on the supply and demand of a ride. Not being able to sell a medallion will reduce supply. Holding demand constant, price will increase as supply decreases.
If a medallion owner is happy driving 10 hours a day, but a potential owner would be happy driving 12 hours a day, the current owner should sell to the more eager driver and supply of rides will increase. If the owner cannot sell, then supply of rides is stuck at a lower level.
If the number of medallions in circulation is constant, the market price of a medallion is not a causal factor in the cost of a ride. The causality goes the other way around.