I think OP's argument is the reason why it's "driving your own car" in those markets outside of denser cities is because operating a taxi fleet is not profitabl

I think OP's argument is the reason why it's "driving your own car" in those markets outside of denser cities is because operating a taxi fleet is not profitable at those densities, in part because of employee protections and other regulatory hurdles, and that removing those protections (and shifting additional costs to the state) is what allows uber/lyft to create an alternative to "driving your own car" in a place where taxis have not been able to profitably operate.