(1) Uber and Lyft have worse unit economics than a taxi company because taxi companies leverage some little bits of scale by pooling fleet ownership costs and insurance.
(2) Uber and Lyft are currently pricing rides at about 66% of what it costs to provide.
(3) There's no loyalty.
(4) There's no indication that people are willing to pay what it costs to provide their service, doubly so if its actually more expensive than a taxi due to efficiencies stated in [1].
(5) Self-driving cars are a ruse in this context; many companies are developing them at the same time and when one gets them, shortly after, the other will too. And so will all the car companies itching to get into ridesharing (I'm looking at you, Tesla).
To my knowledge, while Amazon wasn't turning a profit in the early days, re-investing in growth, they weren't selling you $20 bills for $12 in the hopes someday "drones" would allow them to turn a profit.