I would argue that they've disrupted American urban transportation instead of transforming it - we're still essentially getting around the same way, and taxi services world-wide basically operate the same way Uber does and have for a long time. While Uber has a presence in other countries, the public transit infrastructure is far better supported and taxis operate with similar costs.
I can't imagine trying to take Uber in Seoul, for example, when the majority of the time I could either just take the metro or have a home delivery for most stuff I need, or grab one of the numerous taxis. Or, in my current home city of St. Petersburg, Uber doesn't have much of a competitive edge in price or service compared to the other taxi services, and in most cases, just taking a tram or the metro makes more sense.
Uber's system works really well in places where car ownership is mandatory for day to day activities, simply because there aren't any better alternatives. They didn't really transform urban transportation, they just capitalized on the inefficiency of current taxi services, disrupting the existing market, and quite frankly, unless they start to invest in stuff like the personal taxi drones like what is being demoed in Dubai right now [1], I think they're going to end up with a transportation empire that is irrelevant when you can just travel as the crow flies and eliminate the traffic concerns entirely. Granted, such a future has a ways to go with technology and regulatory work, but so do the autonomous cars everyone is banking on.
And to the side point on your comment, doing something impressive doesn't excuse bad behavior.
They did not transformed all that much, they are taxi service like any other. Where they were actually forced to follow the same rules as everyone else (Germany), they do not have better prices. Basically, they are good in taking advantage of corrupt system and make the corruption work for them.
This one is the key. If it wasn't for corruption and breaking laws they couldn't practice such prices. Plus the fact that they manage to get revenue from both riders and drivers.
