* Price reliability: Prices in most taxi systems follow strict rules. Customers can use this knowledge to estimate what they will spend, and drivers what they can earn.
* Service dependability: Because medallions are limited and prices are regulated, taxi drivers can make a living, and the service does not boom/bust. This means customers are not gouged in good times and unable to find taxis in bad times.
* Non-discrimination: Taxis are usually required to respond to all hails, and to not refuse service because your ride is too short/long.
* Driver tracking: because a taxi driver must have a medallion and follow rules about posting information in/on their cabs, passengers can distinguish between 'taxis' and random people offering ride services. While there may be no built-in reputation system, there is incentive and recourse. How do passengers know if a non-taxi is a guy who makes his living from offering rides, or a guy who just stole a car and is going to rob them? A taxi driver is risking a lot by robbing his passenger.
Many of these points are matters of preference, or can be solved by technology (reputation). Do we, as a society, want to incentivize a stable transit system by limiting the number of drivers or by paying more than 'market' prices in slow periods, and more in busy periods? Do we want drivers to be able to refuse service? If not, how do we compensate drivers who make short/long trips that have low profitability and high opportunity costs?