To me, the innovation isn't using an app instead of a phone call, it's the accountability and reliability. Before Uber, I'd have to call a taxi company at least a half hour before I want to leave. If they even answer the call, the response is always "20 minutes", regardless of how long you have to wait. At least a quarter of the time, the taxi will never show up. As a result, I'd barely ever take taxis anywhere. Instead I'd drive my own car, which meant finding/paying for parking and ensuring continued sobriety, else planning to leave the car and likely get a parking ticket the next day. I guess one benefit of the old way is that I'd plan ahead a bit better, so if driving myself wasn't practical I'd leave extra time to take transit or walk.
If I order an Uber/Lyft, I'm nearly guaranteed a ride within a reasonable amount of time once my request is accepted. Yes, occasionally the driver will cancel and the app will find a new driver, which adds to the time. Sure, the time estimate itself is usually off by 10% or so. It's not perfect, but this experience is orders of magnitude better than it used to be. For the most part I only drive my car when I'm leaving the city or need to carry a bunch of things with me.
If I order an Uber/Lyft, I'm nearly guaranteed a ride within a reasonable amount of time once my request is accepted. Yes, occasionally the driver will cancel and the app will find a new driver, which adds to the time. Sure, the time estimate itself is usually off by 10% or so. It's not perfect, but this experience is orders of magnitude better than it used to be. For the most part I only drive my car when I'm leaving the city or need to carry a bunch of things with me.