I think Uber sees self-driving cars much more as an opportunity than a threat - unless they are afraid they won't be able to buy self-driving cars from anyone but Google, and Google won't sell to them. But I'm sure there will be quite a few suppliers by the time they need the cars [1].
Short term I agree with you, but longer term I'm not sure. Short term, they lower costs massively.
Longer term, a majority of people have self-driving cars. If I live in the suburbs, I either keep it all to myself, or loan it out when I'm not using it. If I live in the city, then I likely don't own a car - but instead call on a car as I need to. These probably come from both individual lending their car, and from groups/companies that are setup as a service.
Either way, these cars are likely to be network agnostic - meaning they'll lend themselves out to Uber, Lyft - whoever. So while costs will go down, it could lead to a big margin compression. Meanwhile, the arms seller (Google, whoever) makes money on each car being sold.
Makes sense, therefore, for Uber to continue to focus on capturing the market - their installed consumer base (and their brand) is their strongest asset going forward.
I think people focus too much on Uber replacing consumer transportation. I think they're going to branch out into transport of goods and eat into the trucking industry in a major way, in addition to whatever they do with consumer transportation. A lot of the commoditization concerns that you'd have with transportation don't apply as much to transport.
I could see people buying "priority" access to the self driving car fleet. People who don't mind waiting or don't need to move around during peak hours would just have lower costs.
Google Ventures and Google are separate arms of the same company. Ventures invested, but Google proper is working on their own service to compete against Uber.
Note how easy it'll be for Google to flip the "Uber" provider in Google Maps to their own service.
[1] - https://www.yahoo.com/autos/s/uber-ceo-tesla-sell-half-milli...