There's also the burden of convenience. A taxi is an instant, summonable affair that ends completely with the trip. A hire car has to be hired and returned to a specific location, you have to stow it during your hire period and you have to fuel it. Beyond the tangible costs of fuel, parking, etc. there's also the opportunity cost. For exmaple, people will pay for convenience of a car to pick them up and take them home when drinking, and they may only need the hire car for a couple of 10 minute bursts but you can't hire a car for less than a 24 hour period. Both of those help buoy the cost of a taxi.

I'm not suggesting you're wrong, but it's not as simple as [hire car] + [driver] = [taxi] from a cost perspective.