The icon to the left of a selection set seems to do nothing. All I ever use selection sets for is visiblity toggle, which is circuitously nested under a hover-then-left-click-then-right-click menu. Why not change the selection set icon to a lightbulb? Or, if you prefer to keep the green icon, make it a visibility toggle switch, going from green to gray depending on the state?
It doesn't need to be intelligent, indicating if some of the bodies in the set are already off or some similarly complex indication system. The icon can just become illuminated again if any bodies/components in the set are made visible again.