For insurance claims caused by the autonomous driver, yes. There are obviously other types of claims such as break-ins and hit-and run-parking damage.Just on the very short run. Insurance is a competitive business. Automated driving that never creates accidents will eliminate the need for automotive insurance.
In some alternate reality where people can subscribe to unsupervised wide-ODD autonomy before 2035, the manufacturer would most likely need to cover AD-incidents and not the car owner.