Earlier quoted context omitted.
I don't think "cheap" was the main factor, at least for me and my friends. Predictable pricing, predictable arrival, automated booking, and an ability to complain to someone was significantly more important. (From what I've read, this happened naturally in other countries, but in US, the taxi monopoly was so bad, we needed something crazy like Uber)
Cheap and easy were the big factors, in roughly equal proportions, with a nod towards cheap. I did a lot of things I didn't need to do and just wouldn't have done at all if I would have had to pay taxi prices for several years while Ubers were cheap. Taxi's were also only easily available in very limited circumstances. Taxi's here worked one of two ways. You either negotiated a price before leaving, or they ran a met…
I admit I'm usually taking public transit while traveling if it's reasonably convenient but cheaper ride-share (or taxi) options can tilt the balance when public transit is complicated/awkward. Rent a car for long distance and rural. (I did start using Uber/Lyft in some situations in areas like Silicon Valley where I would previously have reflexively rented a car.) Around where I live, driving my car is the only real alternative except in special cases. And I essentially always take a pre-booked private car back and forth to the airport.
So, for me, more about ease but if I tended to rely on taxi-type services in cities more, it would probably be more about cost which is probably the case with many people commenting here.