Earlier quoted context omitted.
I have been able to pick up a phone and call the cab company for decades.
yeah, but unless you're in a city like New York (possibly a handful of others) the wait is FOREVER. In Phoenix it was routine to have to wait half an hour or more. Same in SLC. It's awful. Uber and Lyft reduced the wait to a fraction of the time with better, quicker and cheaper service.
Phoenix & SLC are also not cities in which people are likely to rely on on-demand ride sharing. Most people own their own car especially if they care about being able to determine exactly when they engage in transiting.
Further, in all of the non-mega / non-already-has-developed-rapid-transit-system cities I've been in, apart from one single city (San Francisco), the wait time for Uber is on the order of the wait time for a taxi. The difference between needing to call or book ahead to avoid a 30 minute wait vs. a 15 minute wait is utterly irrelevant.
The real reason why Uber succeeds in these markets is that they currently subsidize the rate paid to the drivers and thus compete on price. They also have way better marketing and do a good job of making people think the market for Uber rides is more liquid than the market for taxi rides (though in truth it's not more liquid except in dense areas).
Uber is not profitable in these areas, and is just hoping it can subsidize the losses on most decentralized transit regions long enough to defeat regulatory issues, outlast competitors, and put pressure on taxi services. It's still quite a significant gamble.