That's a really interesting way of describing an artificial monopoly specifically designed to increase earnings for a specific group of rent-seeking, wealthy medallion owners.
It's sort of like describing the De Beers corporation as ensuring the world is not littered with relatively-abundant diamonds. I suppose it might be true, but it certainly is not the point of the arrangement.
I don't support medallions, by any means, but I do support a fair quota system to balance transportation availability with congestion management.
The alternative is people using their cars and having to park it. Or taking their business elsewhere in more parking-friendly locations.
What does your system improve about the incentives?
You don't need be 500k in debt to get started for uber as you needed to get a yellow cab medallion
Once you made that decsion (to mortgage you house to get a yellow cab medallion), you are bound to that job as a serf.... Modern day serfdom, that's what the yellow cab medallion system became to the large cities.
the only way out, was bankruptcy, or hope another person will pay just as much for that medallion. Often local mafiosi types were entangled with the system, and you had to deal with them as well.
Please, lets not glorify the pervious system, as it was much worse.
We can work and make this new system better, and force the large corps to provide more (benefits wise), but returning to the old medallion system is two steps back.
They would need to make more money for that, and I'm not sure the consumer is ready to pay. Taxi fares in many cities used to be way higher with the medallions and ridership was abysmal.
Really, what you find objectionable is not the presence of Uber or Lyft, but the fact that people are running independent businesses, competing with each other.
Uber (and Lyft) simply took over as the established rent seeker. At least with medallions, there were caps to prevent overcapacity in the system and your urban cores flooded with rideshare drivers. There is no such restriction with Uber and Lyft, so their revenue comes on the back of the externalities of underpaid drivers and unregulated congestion.