Pre-Uber/Lyft, either the driver rented the car from 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). Sure back then the dispatch only took a 15-20% cut, but medallion payments took at least a 50% cut on every ride. That money didn't get re-invested or re-distributed as incentives to drivers, no. It went straight to the pockets of the local rent-seeker.
The more I spoke to cab drivers the more it seemed their industry was a pyramid scheme aimed at helping established rent-seeker take advantage of often poor new immigrants. Uber/Lyft 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.
And I'm not even touching the usual pain points and often discriminatory practices of medallion drivers (refusing card payments, refusing rides to non-white passengers and to non-white neighborhoods...).