Show default and protected branch on branches list

Should we show the default branch on the branches list? I think 99% of git users have a concept of a "default" branch, and int GitLab we utilise this to improve the workflow when opening merge requests. The default branch is also automatically protected and used as the scope for issue closing. https://docs.gitlab.com/ee/user/project/repository/branches/#default-branch

This then also raised the point, we tell users that protected branches can be viewed in the settings, but not what those branches or patterns could be. I'm assuming we hide this note altogether for users without permission to view/edit the settings. Protected branches are also usually "special" for some reason or another, maybe it makes sense to have their own list or tab?