Uber and Lyft have caused NYC traffic to slow by 12% since 2015 [0]. These private companies have flooded the public roadways and overwhelmed the infrastructure without any obligation to meter themselves or pay for their fair share of access. I finally understand what the NYC Taxi Commission existed for.
[0] https://www.timeout.com/newyork/blog/traffic-is-moving-12-pe...
Second of all, you bandy around private like it's a bad thing. The reason why these companies are successful is because they pioneered a much more better solution than the alternatives. Take, for example the public service Access-a-Ride [1]. This is the kind of "quality" you get without competition and innovation.
[1]: https://longreads.com/2017/09/01/on-nycs-paratransit-fightin...
There is something called fuel taxes.
Plus in NY state, I believe all TNC drivers are licensed and pay business taxes as well (which is why it's why TNCs are more expensive in NY than other places).