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.)