Not really. Even if we accept your frame of analysis, which begins the moment somebody starts a trip and ends the moment they're done, then regulating taxi quality, driver quality, passenger safety, and paying for effective roads are all relevant factors.

But if the system isn't sustainable, then in the long term customers don't get what they want. So when we're designing society-level systems, we need to think about society-scale sustainability.

Personally, instead of our hodgepodge of retirement and health insurance systems, I think we should just fund a strong safety net out of taxes. That minimizes barriers to entrepreneurship and avoids distortions. But that's not what America had when the medallion system was being developed, so we got what we got. You can certainly propose a change to that, but if you want to be taken seriously, you have to explain how you'll solve the problems the existing system solves, or at least be honest that you're not solving them.