Browsers could pin DNS responses when a page finishes loading so any further requests for that domain will use the cached IP instead of doing name lookups but that would be a PITA because they generally rely on the OS DNS subsystem. It might also break long-running pages that won't failover anymore.

It would probably be easier to simply keep a IS_LOOPBACK flag for every DNS name resolved and kill any connection attempts if the flag changes while the page is loaded. Then you can keep using the OS DNS resolver logic.

DNS might legitimately return a different CDN but it sure as hell won't flip between private IP spaces and the public internet.