I wholeheartedly agree the system wasn't great in many cities before Uber, but it's just a sleek version of what was obvious at the time--it just hadn't been built and the incentives weren't there.
I think you can look at bus/train systems as a comparison. In many cities you can download their app, set a destination, and it shows you what tickets you need to buy. You wave your phone to prove you bought your ticket. In many cities you can see the actual buses live on a map. Many bus stops show when the next bus arrives live. Uber was founded in 2009 and iPhone released in 2007. Google Maps was released in 2005, added traffic info in 2007, and Google Maps shipped with the first iPhone. It wasn't hard to see these pieces coming together--it just needed a lot of work, coordination, and a few generations of hardware and software improvements.
I do think they were the first and were innovative in a lot of aspects. I think their impact on the business of taxiing is way more "innovative" than the app and tech--but innovative doesn't necessarily mean "good" or a great use of resources.