The taxi medallion system was put in place precisely to avoid the inherent race to the bottom that is caused by a low barrier to entry (just need a car to be a taxi) and a fixed consumer base (limited number of passengers).
That is not fiction or speculation--it is history. You can look up the problems New York had before the taxi medallion system.
I am by no means defending the taxi system. It was rife with problems (especially outside the very biggest cities): unreliable pickups, long wait times outside of a very small number of areas, not wanting to take credit cards, bad driving routes to overcharge, and a whole litany of other complaints.
The only reason why the whole system hasn't devolved into a free-for-all is that Uber and Lyft have so much VC money subsidizing ride cost that nobody can get under their prices--they are below the bottom.
The real competitor to Uber/Lyft is the company who can take the existing cabs and cab companies and insert them into an app that does real-time bidding on their end and works like Uber/Lyft from the consumer end. Austin, TX showed that once Uber and Lyft quit sucking the oxygen out of the space, competition and new options start opening up.
However, Uber and Lyft will have to both implode first. And the market can remain irrational longer than you can remain solvent.