I don't think that Uber or Lyft are going to invest in self-driving taxis. The capital model is completely different: Uber and Lyft are by design capital light, they own nothing more than the software (1), and someone needs to buy all of these self-driving machines and then someone needs to maintain them, whereas their current model doesn't do that- they can't offer that to any tech partner.

The reason that you don't see more Waymo areas has nothing to do with rider pool or experience, it is because their tech requires pre-mapping everything with LiDAR several times- the advantage is that if you know what is static (because it was in all of that LiDAR mapping) then a simple difference algo can tell you everything that is dynamic in the environment. (Also, they are just starting to hit cities with significant precipitation- SFO, LA, ATX, PHX are all pretty dry cities, they are going into ATL, MIA, DC, DEN, etc.)

1: With a lot of suspicion that much of their profit comes from drivers not understanding depreciation of their vehicles, something that the accountants who work for Uber and Lyft will understand very very well.

Uber, and to a lesser extent Lyft, has been an extremely prolific investor in the autonomous vehicle space. They're absolutely paying attention to it.

Similarly, Waymo isn't bottlenecked by mapping or rain. I've seen enough of them testing in Seattle and Tokyo, as examples.

Uber spent billions trying to make self-driving work, until they gave up. Not "by design".