Waymo and Uber have partnerships in some cities, like Phoenix, where you can only order a Waymo through the Uber app. So they don't view each other only as competitors, though I have no clue what Uber's thinking long-term.
Also, why would Waymo, in the long term, use Uber for this?
They have the car, the driver, the app/software. They are not gonna share a big chunk of the profit with Uber in long term. The current partnership is probably just a tactical thing for both, not a strategic one.
Uber has tremendous brand recognition and marketing in ways that Google has never been good at. I don’t think it’s the most likely outcome, but I would not be shocked to see Uber take an minority ownership stake in Waymo, use it as the preferred self-driving option, and phase out human drivers in many areas over the next 10 years.
Those vehicles would then be fitted with the human interiors for the high demand periods you state.
It's not a future where Uber is a viable company though.
The interesting thing is that uber loses money on every ride. Waymo charges Uber more than Uber charges the customer.
On Uber’s side, though, this is preferable to losing the entire ride. Uber loses much more slowly by controlling the distribution and losing a few dollars per ride than by losing the entire customer base with no revenue from these customers.