To better support student-led discussions, and discussions led by individuals with a student-based role, Canvas should add the ability to post/participate in Group discussions for a group the individual may not be assigned to.
We created a 'Coach' role based on the student role to streamline the user experience for these individuals (the TA role still sees all hidden course navigation items). While we can give them the Groups - view all student groups permission, they cannot participate in any of the discussions in the group areas except for a single group to which they may be assigned. This could also likely be solved by allowing individuals to be assigned to multiple student groups within the same Group Set, but that presents other issues.
Please consider adding the ability to post/participate in ANY Group discussions to the Discussions - moderate permission.