I've always been skeptical [of self driving] but at this point (after having a few rides with Waymo) it appears that the folks at Alphabet have figured it out already and are coming for Uber. Why is not that affecting Uber's price?
Also, on an apples-to-apples basis, ~46% of Uber's revenue comes from markets outside the US where self-driving is yet to go through its own motions, regulatory approvals, local dynamics, learning (see how autos drive in subcontinent), etc.
Waymo is only testing in 4 cities. Market share is barely scratching the surface. Maybe in a decade, it will be viable replacement.
Later one is very visible and scary one.
Like if you don't live in the Bay Area or one of the very few places outside it where Waymo has been testing, people have never heard of it.
Basically, Uber is everywhere and Waymo is nowhere. Uber achieved dominance by rapidly scaling and being able to fight regulation with venture capital. Waymo hasn't been able to do that anywhere.
You need someone ruthless and aggressive at the top, like Travis Kalanick, Jeff Bezos, Elon Musk or Steve Jobs who basically stop at nothing. Folks who act fast and can take big decisions. MBA business types often get caught up in endless meetings, prevaricating over inessential things.
It's far more likely that Uber buys Waymo than Waymo replacing Uber.