Not a bad idea! My (vaguely) related is to fork a Fediverse app / make a browser plugin that caches and indexes only the Fediverse posts that I've browsed - whether on my timeline or on the explore page or whatever. Then I could search the content I've had access to, and I don't feel like I'd be violating anyone's privacy for caching and indexing the content I've already been allowed to view exclusively for my own personal use.
Obviously, it'd be other problems if I started crawling and indexing content for public usage, but I think using a computer to augment my own fallible memory would be acceptable so I can find the posts I wanted to remember 2 weeks later.