Agreed. I'm native, born and raised, and learned about "gypsy cabs", "car service" and how to hail a yellow cab back when yellow cabs still had "jump seats". Uber has democratized what affluent people have always known, money can buy anything, including someone to drive you somewhere.
I think you need to reexamine the meaning of the word "monopolized".
Having a single state-sanctioned business (and therefore backed by the threat of violence) is somehow less monopolistic than having a free market where the best service provider is rewarded by becoming the most popular and profitable one?
This is a false equivalence. There isn't one and only one State Taxi Company. There are hundreds if not thousands of successful private taxi companies in each state.
There's one Uber and maybe Lyft if you're lucky. In the grey-area taxi market, they might fit the definition of a monopoly. I wouldn't argue that though because I know nothing about that market and reading that sentence back makes me laugh.
Microsoft operated in a relatively free market and was the arguably the best software provider as they were the most popular and profitable one for quite some time. They were also deemed a monopoly.
In strong agreement with task_queue here. The taxi industry is legislated on the city level. Uber is poised to become an international actor, with larger gross revenues than the GDP of many small countries (projected $10bil in 2015).