Phenotype
Radioactive Science Sheep
And there's too much binary morality in Bethesda's Fallout games. I know there's no karma system in Fallout 4, but giving Billy to his parents is clearly presented as the good choice and giving him to the Gunners is clearly the bad choice. This quest would have been much more interesting if the player was forced to make a tough moral decision. It wouldn't have been that hard to accomplish something with grey, relative morality.
The boy's parents could have been poor, hopeless jet addicts that couldn't regularly feed or provide for the boy. Yeah they're his real parents and they love him, but the boy's prospects are gloomy if he stays with them.
Similarly the Gunner could have been interested in recruiting the boy into his militia instead of outright enslaving him. The Gunner could easily care for the boy, but he would have been forced into a life of military servitude - possibly becoming a child soldier later one. Either that, or they would at least give him shelter and a good supply of food if he was destined to be a slave.
The most frustrating thing about this quest could have worked without revising it that much. Just rewrite it so that the kid was only stuck in the fridge for a maximum of 2-4 days and make the moral choices tougher. But alas Bethesda are more concerned with producing cool shit and cheaply making the player feel good about themself.
