What's the great idea? That you can call a cab using a mobile phone? That already existed before Uber. Or is the idea that you don't have to hire those people?
Calling a cab with a mobile phone is miles apart from the ridesharing experience.
With Uber or Lyft, I get an idea of when the car will show up, what the ride will cost me, I know they'll take my credit card, they won't tell me the machine is broken after trying my card-make me pay cash-only to find out the charge did actually go through, I won't get taken on a grand tour of the city to run the meter up, I won't be subsidizing the ridiculous protectionist racket that is the medallion system, I'll get a nice easy-to-use receipt for expense purposes, and the ride will probably be cheaper. I can also order a car for someone else and send them home on my bill with no hassles on either side (sending a babysitter home, for example).
Since most of my rides are reimbursed anyway, I don't even care that much about the cost spread though it is nice to be prudent with the company's money as well as my own. Even if Uber were the same price, I'd prefer it over cabs. Because it's so much cheaper, I use it more often.
To be entirely honest, I'm not the best person to make these "analysis". I never took a cab before Uber because they were outrageously expensive. I took Uber's cabs because they're dirt cheap. All the things you mentioned are really irrelevant to me. (I'm sure you could call a black cab on the phone and ask them for an estimate....?)
And when Uber eventually runs out of VC money, I'll go back to never taking cabs.
You could but sometimes the driver is end up 30 minutes late and you have no way of knowing where they are.
Sometimes the driver shows up, sees your ethnicity and drives off.
Sometimes the driver takes inefficient routes to make more money off you.
Sometimes the driver checks your destination, says its too far and goes away.
There were many problems with the "call a cab and cross your fingers" service in many counties that Uber helped solve
An idea is useless without good execution and there's no real reason to credit people on ideas, lots of people have good ideas but almost none execute well on it. For example there were plenty of online mapping companies available, but when Google Maps came out they completely dominated because their execution was so good. It's crazy to just reduce that down and say it wasn't a good idea just good execution.
They also executed well.
The really big difference for me here in Brazil, is that I can communicate to someone in case the route is bad, something is stolen, etc. Taking a cab is so ephemeral that I don't even have time to complain or ask for help.
The system went like this:
You call some number like 777-7777.
A man with a heavy accent answers gruffly. You tell him where you live and when you want to be picked up. He says "OK", and then you just hope and pray that someone shows up.
It was not a great system at all.