Try it out in San Francisco. San Francisco cabs are horribly broken.
Unfortunately for your argument, while the medallion system does unjustly restrict competition for cab driving jobs in Chicago and NYC, it does not in fact appear to harm consumers. Cabs work in Chicago and NYC. The potential harm of deregulating and devolving controls to unproven technology far outweighs the benefit.
Totally agree SF is where this should be tried first -- it's the US city where cabs are both needed and broken, and smartphone adoption is very high. And the great thing is: that's where UberCab is in fact starting.
However, I expect that if the service becomes popular, both the cab and MUNI lobbies will attempt legislative sabotage, and the SF supervisors are so enamored of paternalistic reasoning it's a real threat to the business.
Unfortunately for your argument, while the medallion system does unjustly restrict competition for cab driving jobs in Chicago and NYC, it does not in fact appear to harm consumers. Cabs work in Chicago and NYC. The potential harm of deregulating and devolving controls to unproven technology far outweighs the benefit.