Pre-Uber, either the driver rented the car to a middleman who rented the medallion from a rich owner, or said owner was selling and financing (most banks won't touch these medallions!) a medallion at a ridiculous interest rate to a driver that planned to use it as his retirement savings (an extremely volatile asset and not very liquid).
The more I spoke to cab drivers the more it seemed their industry was a pyramid schemed aimed at helping established rent-seeker take advantage of often poor new immigrants. Uber brought a breeze of fresh air: Someone could simply buy a car, calculate the depreciation and it's value on the market (since unlike medallions cars are relatively liquid assets!) do rideshare and calculate their profits or loss. They can get out of the game at anytime, and they know exactly how much they are going to get for the car they have should they sell it.
Also, the argument on Uber/Lyft drivers not being contractors since they can't set their own rates and decide which ride they take strikes me as weird since medallion drivers were contractors, had to charge the price set by the city and could only pick-up customers in the (arbitrary) zones covered by their medallions.