That is where you are quite wrong. The regulations of taxis goes way back to carriage regulations in the 19th century. The reason for this is clear: to ensure that the vehicle is maintained, the driver doesn't have a history of attacking or abducting passengers, and that pricing is transparent and passengers aren't gouged.
Taxis are not private transportation, period. They are a form of public transportation and function more like a transit utility. To not offer basic regulation of taxis is to leave the public at large in significant danger of being ripped off, maimed, and/or assaulted.