Ok, so it seems that taxi service in US sucks.

In Europe traditional taxi companies caught up pretty quickly, you can now order taxi ride via app that has UX similar or even nicer than Uber, and you get licensed taxi driver, car with taxi signs, so that you no longer need to stare weirdly at all black Priuses approaching you, and the driver can speak your language, and knows his way around the city. To recap: traditional taxi service is of much better quality than Uber, and only slightly more expensive, therefore much preferred.

The only time I used Uber was in the US, once I came back I don't miss it at all. I don't know what exactly is wrong with US taxi market, but Uber and Lyft aren't the only solution.