If you go anywhere in the world with less strict taxi regulation, you'll run into this. In Prague, my wife and I hopped into a cab only to find that the meter seemed to exist in a time bubble that ran 10x faster than the rest of the known universe.
I appreciate being able to hail a random car on the street and know exactly what I'm going to get. Safety and fraud issues are exactly why the industry was regulated in the first place.
To help users out with ordering cabs Yandex released an app that actually let's you order cabs and shows you pre-negotiated prices, you can pick whichever one you like (economy, premium, luxury). They include user ratings and some sort of due-diligence for taxis to get accepted to their network.
But apart from that, a Lyft-like system has existed in many cities for years. In Moscow just holding up your hand on the side of the street prompts anyone to just drive over to the side of the street and offer you a ride. Most of these are full-time or part-time drivers, but also people getting home from work who don't mind a small detour for a bit of extra cash. At a fraction of the price this is the most popular way for people to get around, although some cars look like they date back into the USSR era.
This is a perfectly acceptable scenario and I think with modern technology the market will start to regulate itself.
This meant that negotiating a price was pretty much out -- I paid what they asked, and had no real way to gauge whether that was reasonable other than asking a local. I also had no recourse if they overcharged -- what was I going to do?
Information asymmetry is a potent weapon for taking advantage of people, whether it involves taxi rates, or just how clean the restaurant's kitchen is, or how fresh the ingredients are. This is why we have regulations that attempt to provide some of the symmetry required for fair exchange.
In the case of Ebay, Uber, Airbnb, etc., technology can replace regulation as a means of providing power to the previously disadvantaged party. And, technological solutions almost always are more efficient than the regulation they replace.
Ever been somewhere where taxis appear to be completely unregulated? It can be a scary nightmare.
Why not enforce regulations on vehicle safety, accurate and fair charging and driver safety and remove the artificial restrictions on the number of people competing in the market? A lot of places outside of the US go with that approach and it can work pretty well.
I work in Chicago and have a condo in the Near West area (basically Ashland and Madison). Cabbies who are already in the area love seeing me hail them for a downtown trip because they earn a few dollars driving where they would have gone anyway without a paying customer. If the industry was un-regulated, I might consider competing with Uber by offering people with less money than time a way to get an inexpensive cab ride from one of these "backhaul" areas. Imagine an Uber-esque service where a senior citizen who wanted to go to the grocery store sometime in the next hour but only wanted to pay $3 for her trip could place a bid for a pick-up. Cabbies who dropped off a premium customer nearby could at least pay for their fuel to reposition themselves for the next premium customer. Everyone wins. It's this sort of innovation which is stifled by laws deemed to be in the best interest of consumers.
Certainly, the initial reasoning for medallion systems was quality of service and safety. As time goes by and taxi lobbyists become more powerful, they find ways to subvert this into limiting competition. Maybe some city councillor traded his vote on this issue to get a park built in his district, or for support in a primary.
It's not like some Big Government Socialist sat down, twirled his moustache, and said "I think today I will limit competition in the taxicab industry".
That might be why they persist, but the main historical reasons that led to the introduction of tax licenses were: 1) to ensure a certain level of scrupulousness and geographical competence among drivers; 2) to reduce safety incidents caused by poorly maintained vehicles (initially carriages, later automobiles); and 3) to reduce taxis' contribution to traffic congestion by limiting their absolute numbers.
The British Parliament introduced the first such system in the 17th century, responding to concerns expressed by Londoners that thousands of "hackney hell carts", driven by unscrupulous fellows and poorly maintained, were overrunning the city.
Of course, there are now alternate approaches, so maybe the idea should be modified. Vehicle safety is today taken care of separately by mandatory vehicle inspections for all roadworthy vehicles. Congestion could be dealt with through market forces by charging tolls to drive in the busiest areas during peak times, as London has already started doing.