The sidebar of SE sites is pretty busy, there are a lot of different elements that are shown there, most of them only in a specific context. There are very important elements there, like the election announcement in the community bulletin, very useful elements like the favorite tags and interesting ones like the Area 51 stats for beta sites.
Then there are those elements I never found any use for, the list of recent tags and the list of recent badges, and the list of related tags when you don't have any tags selected, e.g. on
Those elements should just be removed from the sidebar, they are just not important and useful enough to be visible on the frontpage or the
/questions page, which are probably the most visited pages of any SE site.
The related questions and tags feature are also pretty useful, but they consume a lot of space, it might make sense to display fewer elements by default for those, but add a "more" link that expands the list of related tags/questions. Or maybe this link should lead to a new site showing related tags/questions with some additional sort option, e.g. based on tags.
One might argue that having those elements on the sidebar doesn't hurt, they're below the more important ones and don't really take any room away from those. But the recent debate about the election notification produced some anecdotal evidence that a significant number of user completely ignore the sidebar. Focusing the sidebar on the essential elements that are actually used a lot by users might help to lower the number of users that just ignore everything on that sidebar.
The SE team has certainly data on the usage of the sidebar available, I have to resort to guessing here. I strongly suspect that the "recent tags" and "recent badges" sidebar elements are rarely used at all, but I can't actually prove this.