I've been administering Moodle since the early days and we have approximately 600 active course sites per semester. I have to say that this "feature" has been one of the most annoying and I still, to this date, have no logical explanation for our teachers as to why, when they say No Grade, a grade still appears in the gradebook. What's worse is that when they are using weighted mean of grades they have to blindly make sure that they have their 100% weight adding up accurately in the gradebook with all of these faux assignments that are not supposed to be worth anything but still showing up as 100 (because unlike sum of grades, weighted does not actually add up the grades/weights for you). They see the 100 and get confused and go back and check to make sure they said No Grade. It doesn't make sense to them.
We have a lot of instructors that use the assignment module as a dropbox and it works really well for them. Sometimes the files that students upload are for a grade, sometimes they are not. If there is an option in the assignment module for No Grade then logically it makes no sense to display it in the gradebook regardless of whether or not they want to give that student feedback.
As far as feedback goes, the teacher can enter feedback into the comment box in the assignment module and/or upload a response file, so I still understand the need to push it to the gradebook? OR are you saying that if you do not push the grade to the gradebook the teacher will no longer have the ability to enter feedback or give a response file in the assignment module? If that's the case, then having the grade pushed to the gradebook as "-" would be much better than not having it at all IMO.
I strongly vote with the (No grade/No grade with feedback) option.
As far as implementing that with other activities I think it would have to be looked at on a case-by-case basis? I mean, there is no Grade option in the quiz like there is in the Assignment. The quiz is set up differently with grades/marks assigned per question not per module and then a max grade for the entire quiz so yes, that would probably be confusing.
Thank you so much for addressing this and seeking feedback!!