A few times as a kid I had to take a taxi alone. I knew the way home, but the driver decided to make a lot of unnecessary turns and go this round about way to run up the fair. I was probably in 3rd grade and knew what he was doing but didn't have the guts to call him out.
That varies wildly depending on city, county, state, and (I'm guessing) country requirements. I drove for a few years in a small-ish city, and neither me nor anyone I ran into at the usual spots were self-employed. We all worked for one of two cab companies, making hourly wages plus tip.
Ha ha this happened when I took a taxi to the railway station, leaving Paris after 10 years. It was quite nice to get the "tourist" route early in the morning so I rolled with it :-)