Google has tons of legal resources for their current business. But that doesn’t mean they can spin up the legal docs and relationships needed to run an Uber-like business at the drop of a hat. The type of risk that Google’s lawyers are used to mitigating are simply not the same, and their lawyers are for the most part not the type of lawyers that you’d want to set up a transportation company with international operations. There are some relevant lawyers there, but the vast majority are specialized in software/cloud, not wheels-on-the-ground.
Of course, it would be easier to put together the necessary legal structure now that Uber and Lyft have already both done so. It’s easier to be a follower than a leader. But it would still be much harder for Google than building a mobile app like Uber, which would be right up Google’s alley.
As others have pointed out, Google could scoop up tons of riders in a heartbeat, by announcing a ride share platform publicly (which would get tons of news coverage) and by advertising the feature within Google Maps, Waze, etc.
Google only needs to put together a one-sided marketplace, where Uber/Lyft had to build a two-sided marketplace. And Google already has a connection to billions (at least hundreds of millions) of potential riders.
It would also need to invest in the vehicles and the technology and the maintenance and the garage to store them in and pay the insurance on the vehicles.
All this to try to compete with Uber (which isn't profitable) in a few areas where the legal, political and climate ("we have cars in Chicago but they only run from March 1st to November 1st") options are favorable.
The marketplace is not the biggest issue that Google would need to overcome.
I don't know a lot of people who love Uber, but I know a lot of people who are only ever going to use one ride sharing app. If Waymo's app is limited to a 180 sq. mile territory and only half of their trips are in that territory, they won't bother. The first time the Waymo app tells them they're going outside their territory, it will be back to Uber forever.
Of course, it would be easier to put together the necessary legal structure now that Uber and Lyft have already both done so. It’s easier to be a follower than a leader. But it would still be much harder for Google than building a mobile app like Uber, which would be right up Google’s alley.