I can give you some actual cases I have seen (built) for the purely manual option.
The course is over and the instructor is reviewing final projects and can manually adjust the completion based on what they find. For instance, the grading for something manually marked done was done by an instructor for a group or a teaching assistant, and the main course instructor wants to adjust it.
A student has started a course but has been or is or will be been absent and can't access the site and so the enrolment has been suspended, but they may still be sending in work directly to the instructor via paper or phone or email.
A course is hidden from students because it is used for recording a prior record of learning (and may also be part of a course completion sequence), where various instructors (or an HR staff person) are marking the manual boxes when they get the proof of the prior learning. This completion may then open up other courses for the student to take.
A manual check box is put at the end of the course (in a Label) for the student to check when they believe they are done. This triggers a notice to the instructor to review the student work to verify this. If the student missed something, the instructor uncompletes it and the student reviews and marks it complete again when they have corrected the issue.