I TA an online course with >400 students and a teaching staff of 10. My biggest concern is that when we mute an assignment for grading, someone could accidentally unmute it and reveal incomplete grades or grades that weren't ready for release. While I've explained muting to the other TAs and hopefully they won't touch muting, it would be helpful to have a "mute lock" that would prevent others from unmuting the assignment.
Ideally this would be a course-level setting since courses with a single instructor probably do not need this functionality. It could take the form of a password, or with less overhead, it could only allow the muter, anyone registered with the role of Teacher, or the Canvas administrator to unmute the assignment.