What are the big expenses that cost Uber and Lyft so much? The driver takes the cost of owning and maintaining the vehicle, and they're only paid a fraction of whatever rides they get. Aren't the companies just running an app?
Since they have infinite investor cash (for now), they can do that in many countries at the same time (hence the costs).
All this will eventually crash, and/or Uber will be forced to comply with labor/taxi/etc. laws.
For the most part, established cities are profitable (at least for Uber, I don't know the story for Lyft).
Uber, on the other hand, has several verticals, and also enough muscle to be able to strike profitable deals w/ local competitors, as it has already done in various countries.