> I also don't think Uber's biggest competition is cars or taxis, I imagine it is public transport.
Also worth noting: Los Angeles is not like London or Paris or NYC where you can very often walk to a nearby mass transit station. In many parts of Los Angeles, Uber can serve as a useful complement to the public transport system. For example, one can quickly take Uber to a rail station which then travels the rest of your route underground -- thus avoiding traffic jams.
If Uber did not exist in LA, one would be more likely to just get in one's car for the entire journey: buses take too long to get you to the underground station, and taxis are too expensive.
It's also important to keep in mind that, in Los Angeles, Uber cars arrive really promptly by comparison to public transport buses. If your time in, say, the office, is really valuable, then the Uber service offers more value than a bus, because buses require a lot more time to transport you than an Uber car does.
I know this sounds like an ad for Uber, but I have no connection to the company, except as an occasional customer.