At the US rental companies I've used, CDWs specifically do cover those things, and in fact cover pretty much everything related to any damage of the vehicle (with caveats, like you were using the vehicle for something illegal). I guess the US/UK difference is good to keep in mind next time I head to the UK.

https://www.avis.com/en/help/usa-faqs/cdw-insurance

https://www.avis.com/en/products-and-services/protections/lo...