What's wrong with setting up a mirror at archive.org? After all, they /are/ a library, so they get some immunity from copyright. Or can we not do that?
Pretty sure no-one gets "immunity from copyright," at list not to the point where they could mirror Sci-hub with impunity (at least no on in the US). I'd very surprised if archive.org did not respond to DMCA take-down requests, etc.
This is a violation of the takedown request, and can result in harsher penalties for the host. It's not a great example, but MegaUpload was faulted for doing just that: Removing the link between a url and the content that url pointed to. Granted they did deduplication so there could be other links from other urls pointed to the same "illegal" content, which is what the USA went after them for, but the fact remains that it's a pretty clear grey area whether or not the host can retain that data after someone claims rights to have it removed for their own future benefit.
Then what's the point? The whole point of Sci-hub is to distribute copyrighted papers, "archive" would be inaccessible until it is useless.