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.
In the US, this is exactly how Uber operates. The fare is fixed. It varies by area, but in LA it's about a dollar per mile and 20 cents per min. When you order the uber ride, the driver accepts before he knows where you're going. I've never had a driver tell me "no I won't go there" and I'm pretty sure they would be cut off if they did that.
Your taxi analogy is flawed, because taxi drivers can serve whatever areas they want, regardless of what Uber does.
The main difference in my eyes in why Uber is cheaper is because taxis are set up so people have a career as a taxi driver, but uber is set up for temporary work. So with uber people don't worry about job longevity, or living wage, or health insurance.
But honestly, even if uber were the same price as taxis I would take them way more often because the uber passenger experience is so much NICER. This is a fact and it is a shame that the taxi companies have not tried to step up their game, and instead are looking for regulatory interference to save the day.
Also, it's fair to say that while uber is cheaper than cabs I use the service a whole bunch more, so my total "cab expenditures" in a year is much greater on uber than it was with cabs.
But the biggest point that I'm making is that cabs are 90% NASTY while uber is just 20% NASTY. I like Lyft the best, which is just 5% NASTY.