Not sure I understand. If you're using your ISP's DNS service, majority of your requests are going to hit their cache. You shouldn't notice any downtime as long as the cache doesn't expire.

I mean if all of Google/Cloudflares anycast resolvers go tits up I'm going to get endless calls regardless if the end user can resolve a cached name or not.

> If you're using your ISP's DNS service

Or you can directly ask a domain's authoritative nameserver directly. Using an intermediate caching resolver isn't required. Recursively resolving the DNS query locally only requires asking a centralized nameserver for a domain's authoritative nameservers (the NS records) which can usually be cashed locally for a long time. Every other request is compartmentalized to different servers by domain delegation.

Or do both; configure your local resolver to try recursively resolving a request, and fall back to the ISP (other) cache if needed.