Car rental because you have to pick up the car and later drop it off and the costs are significantly higher than a taxi, and public transportation because it's slower, more crowded (therefore more difficult with luggage) and doesn't always go directly where you want to go.
On a city-wide scale you can't expect car rentals and public transportation to be a valid replacement for a taxi/taxi-like service.
I love that I live in one of the few cities with a train that leaves directly from the airport.
(I now wonder how many others I don't know about from personal experience!)
> and who do you think is paying for your cheap Lyft trips?
Mostly my own contribution, and partially VC money.
1. http://www.cnbc.com/2017/01/12/pipsqueak-lyft-could-reach-pr...
Also public transit, car rentals, etc.