To be clear, California's legislators are paying close attention to Waymo, both because it's being deployed in their major cities, and because Alphabet is a California company.

Depending on which legislator you listen to, Waymo is either the devil that is constantly running people and cats down everywhere, or savior that will rapidly replace all human drivers because it's safer. At least for now, they are keeping a fairly light touch on the legislation for self-driving cars, both because they want to see the technology expand without unnecessary regulation, and because they want to know what the baseline fatality rate is compared to humans.

Likely when the image is clearer (personally I expect that self-driving will expand to all major US cities, and also demonstrate that it is safer than humans) they will find some regulation around remote operator qualifications.