When I was small, some private company wanted to start bus service in my city, but government struck down the proposal. The government buses serve non-profitable and profitable areas. They make profit in one area and subsidize another. Private player would only operate in profitable area causing either a loss or winding down operation in non-profitable area.
Case with Uber is similar. Registered taxi services have to carry passengers at pre-determined rate. Sometimes it is not profitable specially if a customer stays in area from which you don't easily get return passengers. This gets compensated when you customer and return as well. With Uber, they will charge more or less based on the analytics and eventually registered taxi drivers would lend up serving less profitable areas and more profitable routes will be undercut by Uber. If Uber is allowed, it should have the exact same requirements: Publish fare, must take customers at this rate irrespective of where you want to go and should take passengers strictly in the order in which requests are incoming. Otherwise, it is giving unfair advantage to Uber over taxi service.