Earlier quoted context omitted.
There are many existing, one that is supported by the local taxi drivers in my city would be http://www.taxi.eu/en/
Well, now I have to admit confusion. I downloaded it and poked around, and it seems to be put together pretty well and has all the features from Uber. My best guess is that they started in a place where taxis were generally "good enough" already and didn't market it as hard, but it definitely competes well along the dimensions I gave before.
But you have to know: My region had a dozen of these apps, all competing with each other.
So, the only reason why people used uber was that sometimes it was cheaper. But that only because they ignored the laws.
German Taxi market is a seriously free market, and uber can’t compete fairly.