It's less than that—they provide the ability to call taxis from an app. You've been able to call taxis from phones for significantly longer, you just had to dial a number.
I know this isn't a common way to call taxis everywhere, but it was in some locations. I went to college in a small-ish city called Saratoga Springs. If you wanted a taxi, the expected method was to dial one of the local taxi companies. They'd arrive in a few minutes. It was a little more expensive than Uber and Lyft, but not drastically so, and while I'm sure a bit of that price difference comes from increased efficiency, I think a lot of it is just VC money.
I probably called 3 cabs total before I was aware of uber, and my experience each time was wait for around an hour, even if you had pre-arranged the pickup, and when calling the dispatcher, they would just say the cab was 10 minutes away, no matter what was actually going on.
My impression is that taxi companies, wanting to be profitable, keep the largest number of drivers on call that can be maximally utilized -- not the smallest number needed to guarantee a certain SLO. So when you call dispatch and they tell you "30 minutes", that's a bald faced lie. It's not that the taxi driver got lost or stopped for a coffee break on the route, it's that they did not have any taxi drivers available for the next 80 minutes, and knew it.
The drivers don't get punished because they did nothing wrong; there may have never been a driver assigned to go pick you up.
It's like when you go to the grocery and there is one checkout open and ten people in line; it's not that the cashier is slow, it's that it is more profitable to make you wait than to have two cashiers sitting idle after you leave.
Uber gave everyone access to information about the cost of taxis - and generally people found it wasn't as expensive as they'd thought.
It's likely not true for all areas or countries but here Uber provided so much better experience that I would use it even if it was more expensive. It's the best thing that ever happened to taxi customers here as now many other players implemented apps with similar features to Uber. Even if they go bust I will remember them for making my life much better.