When students self-enroll into a group, it would be nice to set availability dates for when they can self-enroll and be visible to specific sections too.
The reason for availability dates is so teachers can do group creations during class or at a specific time of day. Then those groups are locked and can no longer be changed (except for the teacher). Having to always remember to turn on/off the self-enrollment button will create more issues and potential for students to jump groups when they should be submitting an assignment with the group already set/locked.
This also helps if multiple class sections are in one group set. This way one "class" is locked out after class is finished. Then the teacher can open it for the next class period.