The lease for the cab was high enough ($600+/wk) that I had to drive ~30 hours to break even, and the rest was profit, usually another 20 hours over the weekend.
Unless you were sharing a lease with another driver, it would've been impossible to work it as part time.
So I would see a benefit to uber over that arrangement except for uber if your car breaks you're out of luck. With a cab, i'd take it to the shop and get another one. Granted they were all pretty beat up crown vics.
The real winners were the owners of the cab company. Like you said, they held the medallions and thus most of the leverage.
It makes sense in the comment above, as the cab driver actually has work expenses that they pay for out of pocket and are not reimbursed for.
Uber drivers can rent their car by the week.