There is yet another use for C810. Remember that you must be "in continuous enrollment" once you have passed your PhD exams and become a candidate? This does not usually require summer enrollment, but here is one important exception to this.
If you end up defending and/or submitting your dissertation in the summer, you must be enrolled during the summer session in which this is accomplished. Further, remember that G901 is not available during the summer? If you are defending or submitting your dissertation in the summer, you will need to enroll in one hour of C810 for that summer session.
Frankly, imo, this is another great reason to avoid finishing during the summer (more on that at a later date), but sometimes it just can't be helped.