I agree with your underlying premise that in the (very) long term, all taxis will be automated; I guess the gamble for investors is how long that transition takes, across the globe.
This. Uber can operate anywhere that has human drivers and cell service. Waymo needs (I think) high-precision maps that are frequently updated, and simple traffic behavior.
Traffic in Lima looks like absolute chaos to an American, with endless honking and lane markers treated as vague suggestions, but there are not constant crashes, because the (mostly professional) drivers know the local conventions and communicate with each other by horn, eye contact, hand signal, etc. Huaraz is full of blind 4-way intersections with no stop signs, so drivers honk as they get close to one, and there is a remarkable lack of fiery death.
Waymo can't work in most places until it either changes human driving, or achieves AGI. Uber works as soon as it can pay local drivers.
I'm saying a Jaguar I-Pace with lidar that knows how to follow lines and a high-res map isn't suitable for a lot of the world's roads. And how it will "scale" to what a taxi can handle right now isn't at all obvious.
Plus drivers will learn the weaknesses of self-driving cars and then abuse those weaknesses.
Taxi drivers know not to stop in certain unsafe locations - good luck for self-driving cars to learn how to read for dangerous situations because of criminals.
I think there's also the fact that if self-driving cars take off and price goes down, people will ultimately rely on taxis/delivery more than ever. Maybe there is a place for Uber to be the platform for that still, maybe not.