One workaround (requires Asana Premium) to the can’t-complete-a-section is:
Instead of using actual Sections, use a custom field, perhaps called “Section”.
For each new “section” add a dropdown value for the section name. (This can be cumbersome if you frequently create many sections, but if not, you may find this workable.)
One time only: Sort (which is actually grouping more than sorting) the project by the “Section” custom field and then Save layout as default.
Now, the grouping “Section” values will come and go automatically based on whether they have entries in them. For example, if showing only Incomplete tasks, and their are none in a section, then no header for that “Section” will appear. But if you change the view to Completed tasks, then it will automatically appear because now it’s needed again.
I often use a custom field like this instead of using Sections themselves in certain cases, including those where I might want to sort (group) by another field (say Assignee) at times and I don’t want two levels of headings appearing (Assignee heading > Section heading(s) > tasks).
Hope that might help someone,
Larry