I don’t think it’s solvable if users don’t themselves close or group/categorize the stuff they’re opening. Any automation/heuristic is prone to not do what the user wants, because the tool can’t really judge why the user opened any given page, and thus can’t make an informed decision in how to handle it. I can think of new (mostly power-)user features to support the user in organizing opened pages, but I have a hard time imagining an I-don’t-want-to-deal-with-this user feature that would universally “just work”. (Of course, I may be wrong.)

The closest I can think of is to have sortable list views of open pages that you can sort by open date, last updated, possibly content type (e.g. has video), and/or group by site or by “opened from” (navigation history graph). Again, this is moving into power user territory.