One alleged evil of "excessive competition" here is that with open competition you might get a "race to the bottom" wherein cabs that aren't well maintained or that overcharge customers make the most money. The initial apparent advantage of the medallion system is that it gives the regulators quite a lot of control over what cab operators do and it's easy to imagine that power might be used to do good. Standardizing cab appearance and fares so customers aren't confused, standardizing cab behavior in various ways, that sort of thing.

The downside of this system is that - like nearly every other regulatory system - it is subject to "regulatory capture". Over the years, the established players in any regulated industry have a huge incentive to convince the regulators to rule in ways that keep out competitors. Eventually market competition no longer serves as a check on bad behavior at all - all that matters is keeping the regulators happy. And the regulators are in the pocket of industry, so customers get screwed.