This idea has been developed and deployed to Canvas
Situation 1: As an instructor or course monitor you manage multiple sections of a course on a single Canvas page, you are the instructor and grader for all sections.
In my case this can be two sections of one course where I am teaching and grading both sections myself, however the two sections meet different days of the week (Tuesday vs Thursday). The Assignments feature already lets me set available and due dates independently for each section while creating only one assignment, which shows in the gradebook.
However, when in the gradebook if I want to mute the assignment until I'm done grading all of them so students get feedback at the same time (and I don't get barraged with emails mid grading) my only option is to mute all sections at once. Ideally I would like to be able to mute sections independently so I can grade the Tuesday section's assignment first, and unmute it first so they get their feedback by Tuesday. At the same time the Thursday section would remain muted longer since I have a few more days to finish up grading that section. Unfortunately the only option right now is to mute all sections and get all the grading done earlier than it needs to be, or don't use the mute option at all.
Situation 2: As an instructor or course monitor you manage multiple sections of a course on a single Canvas page. You are the instructor for all sections, but you have a different grader or Teaching Assistant for each individual section.
In my case this is 10 sections of one laboratory course where a graduate student is the Teaching Assistant and Grader, there is a different graduate student for each section so in total there are 10 different graders. Each Grader/TA is assigned to only one section and has been added so they "can only grade the section they are enrolled in."
Once again the Assignments are created as a course wide assignment with independent availability and due dates for each section depending on the time they meet during the week (T-Th). Each grader only has the ability to see their section's grades and grade only their section's student submissions. However, when the individual graders use the mute/unmute assignment feature (without their knowledge or ability to know) the mute/unmute is applied across ALL sections. This is opposite what it should be. If they can only interact with grades from their section any mute/unmute they perform should only affect their section.
The ability to mute/unmute assignments in the Canvas gradebook is clearly a beneficial and useful feature. It keeps feedback fair and equal for all students, it by default notifies students when an assignment is unmuted and their grade is available, and it frees the instructor/grader from having to respond to grade questions before finishing grading an assignment.
Unfortunately as it is right now, it is mostly useless for multi-section courses managed under one course page. Changing the mute/unmute assignment feature to be applicable course wide or by individual section would greatly improve its usefulness.