What I envision is the same functionality that is available with People and custom attributes, allowing the same for Group Scheduler. I would like to add custom attributes to the group and when a person is added to the schedule, these attributes show up in a modal popup to edit and applied to each individual. These attributes will be applied to what I believe is the underlining Attendance record and then can be displayed in emails and the Group Schedule Toolbox block.
For instance, for our kids ministry, I add a Role attribute (Teacher, Check-In, Small Groups, Games) to the group. In the Group Scheduler, I drag a name to the location/time section and a popup opens and provides the ability to select a role from the custom attribute that was added to the group previously. Or for greeters, the attribute may be location (North Door, West Door, Parking Lot). For a Small Group, it may be Role (Devotional, Prayer, Host). The Group Schedule popup should be dynamic to show attributes that were added to that particular group. I believe everyone can find use for something like this.