I simultaneously thought of a name and how that name can inspire game play. The name is Meltdown. The inspiration is to have the balls duplicate themselves and split after a certain number of bounces. If the density of balls exceeds a threshold, then the game undergoes a meltdown (and the game is over). To avoid a meltdown, players need to let some balls go into the pockets. But if they let all of the balls go into the pockets, then it is game over as well. It probably needs some work (perhaps balls should split after X bounces, change color, and die after Y additional bounces), but that sounds like a good start.
(Balls could be neutrons. Bumpers could be fuel rods. Hmm ….)