Uh, most people (and the TLC itself) are ignoring the distinction between medallion cabs vs car service/'black cars."
Medallion cabs: yellow, spend $1mm for a medallion (a bit cheaper for an "owner-driven" medallion, where the owner promises to drive one shift a day), have meters with regulated fares, famously won't usually take you out of Manhattan, and cruise Manhattan/Downtown Brooklyn, looking for street hails.
Car service: not yellow, almost anyone can get a license, not allowed to pick up street hails (MUST use a base/radio), go anywhere/pick up anywhere, and charge whatever they want.
Uber is targeted to the latter.