1. Same interface in any city. I don't need to figure out what the taxi phone number is (or what they are in case of multiple companies).
2. I can get a car somewhere other than downtown.
3. I can pay with credit, without fear that a driver will (best case) lie that the credit card machine is not working, until I say I don't have cash, or (worst case) kidnap me and take me to an ATM.
4. No silly medallion limits, so I never need to wait for long, even at closing time.
They really don't need to do the Ponzi scheme thing, hemorrhaging money and leaving the VC with the bill. Plenty of people will gladly pay more than a cab for the above benefits. In that sense, taxis are not really a competitor.