Uber and Lyft operated partially or outright illegally in many places while negotiating with governments. They also had a far superior product. Just like they fought the existing taxi companies, Waymo will have to fight against Uber and Lyft's lawyers, who are probably better funded and have learned to become better entrenched in governments.
Lyft + Uber market cap is under 200B Alphabet 4T+ I think they will manage
Uber and Lyft are goners, their customers don't care about them and will take Waymos the second they're available.
Uber and Lyft will survive exactly to the extent they successfully adopt self-driving.