Well for one, they don't actually host anything on the site itself. Anna's Archive is technically just a search engine for searching through backups of all the Libgen mirrors and Zlib. Since they made a point of scraping and backing up these shadow libraries, even if those sites themselves (and Anna's Archive) go down, the backups will still be available. That on its own makes it a thousand times more useful to me than any single shadow library site. The backups are also hosted on IPFS and available via large torrent files, meaning anyone can download everything they have backed up and since their site's code base is open source, anyone can fork the site and rehost everything should the need to do so ever arise.

They seem to have a very sophisticated system in place for ensuring that everything they've hosted will always be available no matter what. It inspires a lot of confidence, in my opinion. I personally don't think they'll ever go down, or if they do, a different team can pick up the slack by rehosting everything on a different site.