The limited medallion system isn't perfect. It unfairly limits who can drive a taxi. However, it is important to do so because otherwise the supply of taxes will be out of control. Traffic will be out of control. Individual taxi drivers will make less money if supply gets too high. It needs to be limited.
More important is the system of licensing. Taxi drivers have to go through special training. In London especially, actual cab drivers have to have extensive expertise. To drive an uber you don't need jack shit.
Taxis are also regulated in many other ways we have already discussed. Consistent fair pricing. Meters that aren't rigged. Requirements to pick up anybody and not deny a ride. Requirements to pick up handicap people. Requirements to take people wherever they want to go. Even if these rules are not enforced perfectly, they still exist, and should exist. Uber and others simply ignore them all.
When Silicon Valley sees an imperfect system, their solution always seem to be just to remove it and replace it with nothing, or replace it with the free market. If something is imperfect, don't toss it out, just fucking fix it!
Sadly, fixing things is actually hard work, and doesn't help with get rich quick schemes.