If I get into a cab, the driver asks where I am going, and I stump them by naming a major hotel, I personally feel like that was a frustrating failure, as now we are stuck in an intersection while I try to teach them the layout of a city I know less about than they do: the reason I am hiring a cab driver in the first place is because I want to outsource transportation, and the power that comes from being able to a street hail a cab to anywhere I want to go is tremendously useful.
The way I would describe the benefit is that "if I am using a cab it is generally because I don't know where I am or where I need to be". Imagine if you went to a restaurant, ordered a sandwich, and the waiter was like "ok, I can make that, but can you tell me what goes in it?" or hire a consultant to build some software for you and they say "ok, I can type that, but how do I build this?".
The real problem in San Francisco is that it was impossible to street hail. Your best strategy was typically to go to a nearby hotel and tip the valet to flag you a cab. Even then you were effectively screwed. And the dispatch at every cab company I have ever dealt with (except for Radio Cab in Portland) is a mess, and often they just lose track of fares.
What Uber and Lyft provided is just software that they could have sold to the cab companies to replace their dispatch, which would have solved these problems and worked in the existing ecosystem, but they wanted to take over the world and vertically integrate. I can see why, even if it frustrates me that we live in a world where that is even possible, as I do not see them as net forces for good :/.