I see your point, in theory, but the increasing medallion investment/rent just lowered profit further and further until the profit to drivers was some very low wage. The driver is not usually the medallion owner, and hence the rent for the medallion goes elsewhere. The driver just ends up with the metered fare net of medallion costs.

Similarly, Uber leads to a sort of perfect competition equilibrium (https://en.wikipedia.org/wiki/Perfect_competition) where drivers keep entering the marketplace until wages drop to some low wage, but not below that (because below that, drivers start to leave the marketplace, thus decreasing supply and increasing the equilibrium price point.)

Actually it's more like a monopsony where a single buyer (uber) can dictate the price to the sellers (drivers). Uber varies the prices it charges consumers (and therefore pays drivers) based on what maximises its profit rather than general economic welfare.

Economically, it does lead to a competition equilibrium, but it does not take into account the cost of externalities such as additional traffic and pollution generated by having more drivers.

At appropriate saturation the number of cars being displaced by riders is significant, though I wonder what that is and how it trends over time.

If I was in college today, I might never consider buying a vehicle.

No. What happens is that roads keep becoming saturated until they are clogged with ride shares and the riders bail out when they realize they can walk faster. The equilibrium point creates complete havoc for everyone else and little productive work is actually done.

The roads are already clogged with cars. Does it matter if they are ride shares or not?

A saturated Uber-model ride share market is one where an empty car is seconds away whenever you need one. Idle ride shares matter a lot.

Or it could be a model where there is always a car with a ride share available.

I mean could it be the Uber Go model is the best win-win for the customers, Uber and the drivers?

Taxis (drivers) don't make money, or rather, they are subjected to the same degree of commoditization either way.

Medallion owners make money. All of the profits are extracted into the medallions.

It's actually a bad system, really.

'Driving a taxi' is a total commodity, there's a limitless supply of people willing to do it for sub minimum wage, so the money just goes to the owners.

Rent extraction is usually a bad way to manage things; it's kind of like real-estate speculation, but there's no need for it.

It'd be nice to see the cities embrace Uber-like systems, capture the profits from it, enforce basic laws, and somehow make it fair. I'm not holding my breath.