I notice that to see someone has added a draft on to your story, despite it being your story, it does not appear in the story map or in notifications until published. i recommend allowing them to be displayed to the stories owner at least without hunting for them
I agree. But I could imagine that the story owner deletes half-done chapters if they aren't aware that they are drafts. So the labeling should be obvious. (Firefox had a bug that hid the label underneath the next line, so every chapter looked like it was published.)