You could already call taxis by phone (including your mobile), as you say. So you are creating something of a false dichotomy. At least where I live, there are also public devices (only in particular places, of course) you can use to hail a cab, in case you somehow don't own a mobile.
And apparently mytaxi was founded the same year as Uber, so Uber's idea wasn't quite that unique. I suppose it was just the right time for such services to spring into existence.
Uber appears to be the most successful, probably in no small part due to their ruthlessness.
I've never ordered a taxi in a small town, so I can't comment on what that process is like.
I'd guess I've called in for around 10 cab rides, and have had two experiences where a cab was requested, I was told it would come, and had it not come after waiting for much longer than was reasonable.
Uber doesn't actually show you where the drivers are before you request the ride. Those little animated icons just represent the density of available drivers, not actual car positions.
(It just sounds really dishonest for the app to do this)
It was neither difficult nor traumatic as the descriptions of the "problem" that Uber is solving that I see in these Uber threads. I've never driven a car in my 40 years of life, and therefore taken 1000 cabs in a dozen cities, but I've clearly only taken the best ones.
Maybe things have changed since the introduction of these ride sharing apps, but reliability of the Baltimore taxi system used to be atrocious outside of the 5 block radius of the Inner Harbor.
If you had said "black car service," I would have believed your story could be representative, but that is simply incongruent with every experience I've had in Baltimore. I tried the 3 major cab companies in Baltimore and had similar experiences with each.
I'm not alleging any moral shortcoming, it's just that there was no incentive to improve service to an acceptable level until Uber and Lyft arrived.
It's a cab company that decided to ditch the cabs and to "contract" with "independent owner-operators" in an effort to circumvent the laws around cabs, and to avoid the hassles of actually having employees and capital expenditures. It's just the Web 2.0 business of plan of "let the users provide the content, and then sell it back to them", applied to physical objects.