>The self-driving car game was supposed to save them, but I don't think they're guaranteed to win that fight
Agreed. I'd argue that existing car-sharing companies like Car2Go are better positioned to dominate the "self-driving taxi" market. They've already solved the challenges of owning and maintaining a shared car fleet profitably. The day self-driving technology is ready, they'll already be miles ahead of Uber.
When driverless tech becomes available, they'll be much better positioned than Uber.