Just because it’s big doesn’t mean Google will inevitably succeed. Look at Google+, Allo, Duo etc etc. to my mind there’s no guarantee a Google rideshare app would capture mindshare.

Google is so much more integrated in to people's lives than 15+ years ago. Google Maps + Waymo or "Google Taxi" would have millions of customers immediately.

What Google did to Yelp is what might happen to Uber. I think the main point thing stopping is what others have pointed out. Is it worth the reputation? Instead of running their own service just take a nice cut from Uber and let them deal with bad headlines. Especially when the headlines will read Uber "fires" poor single parent uber drivers in favor of robot cars.