If I offer you a ride to the airport for ten bucks,should the state prosecute me criminally? Or is that true only if I use the I Internet to do it? What if I post in an online forum?
The state can certainly require me to purchase insurance to own a vehicle. Clearly in the public's interest. Perhaps that insurance should cover riders. Great discussion. But this is simply crony capitalism. There may be risk, but there is no crime here. At all.
That's not to say there is no "public interest", but rather that the public interest is something that has to be balanced against other interests, and the freedom to ply a trade is a pretty important one.
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.
Those days are long gone, however. Today I can buy a used car on Ebay, committing thousands of dollars to a sale for a product I've never seen and a seller I'll never meet, all without worrying about the transaction. Why? Because information flows much more freely. The commercial transaction that used to take a government guarantee now just requires an open exchange of information about past history -- which is trivial to accomplish.
The 1800s are long gone. Time to move on.