> the capital costs of entering the taxi business are low.

Is what I suspect is the key point. Because capital costs are so low, it's easy for anyone to get into the business. Because it's easy to get into the business, you end up with lots of turnover as people come in looking to charge high rates, get tired of it, and move on to some other job.

Medallions artificially raise the capital costs involved in becoming a Taxi driver, and therefore make people more likely to continue as drivers, since they want to recoup their initial investment, and it's not trivial to do so.