This plays into their "Uber vs. The Taxi Cartel" trope perfectly. In reality, Taxi regulations vary by city, state, and country. Uber is now operating in over 90 cities in the US and in 44 other countries. They couldn't possibly be "forced to close at any moment" since their business is legal or at least 'not illegal' in the vast majority of those territories.
The "Taxi Cartel" is really several hundred independent locally granted monopolies that exist to attempt to ensure requirements that Uber is going to ignore. The highly profitable airport routes exist to subsidize the requirement that taxis are handicap-accessible and can't discriminate against customers. Medallions were created to ensure that cars were properly maintained, drivers could earn decent wages, and that there wouldn't be reoccurrences of the crime waves against taxis and customers that led to medallions in the first place.
Obviously the number of medallions has been restricted to an unreasonably small number in most places causing the terrible service that many are used to. Also fairly obviously, the advent of the smartphone with personal profiles has reduced the crime potential facing the typical cabbie as well as the issues hailing cabs in outer boroughs or less populated neighborhoods. All of that said, it's not like cab companies or taxi drivers are widely profitable. The only public Medallion company (NASDAQ: TAXI) only makes $35M in revenue/year and about 1/3 of that in net income. If the claims surrounding Uber are true, they're projecting close to $2 Billion in net revenue in the very near future.
If Uber does indeed take all of the profitable routes, Taxi companies will close their doors. Some might consider that a net win, but consider the Uber app and the demographics of Smartphone owners (http://i.imgur.com/T5JpmQE.png) and then try and estimate how many Ubers are handicap-accessible. This would only be a net win for the wealthy, young, and non-handicapped, which was the entire point of taxi regulation in the first place.
I don't mean to argue that Uber = Bad and Taxis = Good, and there are other options to solve these problems rather than local monopolies and route protection, but the simplistic "Uber vs. Taxis" analysis usually ignores all of the externalities that would accompany a taxi-less world.