We'd like to be able to assign a privilege to a custom role in ArcGIS Online that allows a little more than inviting members to groups that a member owns. Administrators are able to assign members to any group. We'd like to see a privilege that allows group owners to assign (rather than just invite) members to their groups. Perhaps include a notification that "you have been assigned to a new group: "Group Name" owned by "Owner's Name".
This would make group management workflows much simpler for group owners - especially when adding a lot of members to many groups. No need to follow up with people who haven't accepted invites, yet those same people are free to remove themselves from groups if they choose.