Remember that Mediawiki (MW) is not just Wikipedia (WP and co.) I run several MW instances and the sitewide sidebar is fully customisable which is handy. Many users are used to the LHS holding "tools". You could also/instead put a hierarchy tree of say categories in it.

I'm not absolutely sure but I think you might even be able to create your own user version of the sidebar if you create a suitably named user page. I'm not sure what WP sites allow you to do but MW has a lot of user customisation options built in.