That would be different based on the city and state (US)
A friend drove a cab for years and around here that is not how it works. The cab company rents the cabs to the drivers at a set amount per day. The driver can accept jobs that come in across the computer but there will be a small handling charge that is built into the price per mile printed on the side of the cab and used in the meter. If they pick up some one who flags them down or some one who calls their Cell and requests a pickup then there is no handling charge.
The friend of mine that did it treated it like a small business. He had cards made with his cell on them and kept his car immaculately clean. After the first year 90% of his calls were from customers and word of mouth. He would also give discounts to his regulars. Really the discounts were nothing more than him deducting the handling fee from the printed cost.
I don't know enough of the facts & details of the particular situation you describe, but just from your description, that's not too bad. Especially if the driver rents the cabs and pays no maintenance, insurance, tags, etc etc.
Sadly though, that's not typical in many urban/suburban areas with denser populations (where taxis are needed most) in the US. Most often, you see some sort of local taxi commission that's usually corrupt "regulating" a small number of taxi operations, sometimes just one.
NY's system is one of the most infamous, with Chicago's corrupt system at their heels with Washington D.C. in there too, vying for "Most Corrupt & Broken US Taxi System". Many others are equally bad, heck, I haven't even mentioned anything west of the Mississippi, and there are no lack of bad & corrupt taxi systems!
What's happening here regarding the new online independent private taxi services is really not much different in principle to what has and is happening to the old business models for media/news/entertainment monetization, sales, and distribution.
This time, there are a lot of locally-powerful corrupt politicians, bureaucrats, and unions in major cities around the world that stand to personally lose out if the old taxi systems go extinct, never mind the corrupt taxi company owners' anger and resistance.
The politicians and bureaucrats, as is typical with government (and the larger it is, the more "inertial resistance" to change there is), will have to be brought kicking & screaming into the modern age. This is particularly true if that change means those in government lose money, power, and/or control.