I would loooove this. Open one of your bookmarks and you can't tell it's the local copy unless you looked at the local path sitting in the URL bar. Maybe make an option to fetch a live copy though for sites like the front page of HN that are in constant turnover, but it would be great. Storage has never been cheaper, let me hoard!

You can even take it a step further and create a viewable timeline of all the pages you've visited in case you have something at the tip of your tongue, but need to retrace your steps and logic to get there. Browsing history is kinda lackluster for this. My last ten entries on firefox are three hackernews articles with "Add Comment" dispersed half a dozen times in that list. If I had something along the lines of zoteros timeline for papers I could probably find stuff way easier.

HTTrack does most of that, minus "seamless". You could probably write an extension that automatically sent bookmarked urls to HTTrack for mirroring/archival, then they would all be browsable offline.

You can't seamlessly replicate a REST server.