The few experiences I've had with local Taxi systems, coming from a everyone-drives-a-car suburban background, have been awful. Overcharging, credit card machine breakdown, and unreliability of driver arrival estimation have made me seek out more expensive alternatives, just to avoid the hassle.
I now live in a city where I take public transport 90% of the time. But that 10% has been made so much easier by Uber and Lyft(they offer the "same" features, so they are the same in my book). They tell me; How long until the driver is here(often incorrect, but only by a small factor), how long the trip will take(often incorrect, by only by a small factor), and how much it will cost(often correct or guaranteed).
None of the features above sound unique to Uber/Lyft, the only difference between them and Taxi's are subsidization by Capitalization. I've heard of Flywheel offering the same app features Uber/Lyft do, but Uber's are often under ~$10 where I am, which a Taxi can take anywhere from $25-$45. But if Uber's subsidization goes dry, as long as there's an feature-like alternative, I'd still pay for that.