EDIT: now to mention the unavoidable legal issues, which to a certain extent are similar to what Uber is already dealing with and "resolving" quickly according to reports.
If Google dumped billions into a self driving cab fleet and offered me 30% lower prices than Uber, would I switch? Yes, probably. Do I gain any benefit from my friends being on Uber? No.
For example, what if Uber "builds" (finances and badges) their own car, and you really like it (no reason it can't still have a steering wheel). What if they are willing to enter a one year agreement where it is cleaned and parked in your driveway at 4AM every Mon-Fri morning to take you to work when you're ready. Or if they have a parking lot near your office with 100 cars where you can just walk up to any car, open the door, and go. Or if they have an automated electric vehicle charging network over the whole country. It will take a while to discover what really matters for a AI-car network.