@Pandora_Layn I used to be an English major, literature and story are some of my favorite parts of gaming! Glad to see somebody else who enjoys a good read too.
It's true all we know is that something bad happened. My first thought was since it's set in the 1960s, it could possibly be related to World War 2, but your idea definitely takes it to the next level. The lack of children would make sense with your theory. I read an article about somebody who had hands-on experience at PAX mentioning some storefronts were obviously boarded up but painted over to look open, and that a guard beat a man to death in front of you near the start and then says he'll fetch a doctor and the guy would be right as rain.
It's obvious Joy was born out of necessity but led to the state society is in now. What could launch a society so deep into denial that they'd rather take drugs that negatively impact judgement and mood than face what happened? Your theory of a deal, possibly spearheaded by Uncle Jack, could be that! Perhaps World War 2 went very, very sour in this timeline and a biological weapon was launched that wiped out a majority of the worlds (or at least, Englands) population. Perhaps the people of Wellington Wells were left disparaged and in debt after the war, forcing them to negotiate with surviving foreign bodies for precious commodities. Food, water, youth.
I know at this point we can only speculate. Food and water seem to be somewhat scarce from gameplay reports, which would support the theory that sacrifices had to be made to procure what little people do have.
Uncle Jack is the curious point for me. What is he? A puppet speaking the word of hidden political bodies trying desperately to keep what they have left in tact? The ring-leader? Wellington Wells is going to be a very interesting city to explore.
The missing children could mean nothing and everything. World of Warcraft has child NPCs but they're unkillable. Maybe they wanted to leave children out of the gameplay mechanics since it seems at some points you may have to kill to survive, or it could have much darker influences. Maybe with Joy nobody wants to have kids. It's possible the catastrophe that wiped out a large portion of the population also left most survivors sterile. The people of Wellington Wells could be facing the extinction of the human race, which would make anyone want to take some Joy and forget.
All we can do is speculate, but that's one of the most exciting parts of storytelling! I'm going to have to read through The Ones Who Walk Away from Omelas by Ursula K. Le Guin to get a better understanding of what you mean, but from what I grasp right now, I can say it would be a killer addition to the narrative! Definitely something that would take the game to the next level for me.
They mentioned books like Clockwork Orange and 1984 being influences. The scene in 1984 where the wife tries to kill herself but doesn't seem to recall why or feel anything about it comes to mind when I think of We Happy Few. That extreme denial of feeling ones emotions in the name of forgetting everything. And the teenage girl who was a bit different and ended up being killed by random kids her age going out shooting guns in the streets. I see 1984s influence heavily so far. It's been a while since I read 1984 so forgive me if details are fuzzy, but I see similarities between dystopian societies that are trying everything they can to avoid things that I consider part of the human experience.
Sorry for the wall of text! I can go on for hours about storytelling. TL;DR: Your theory is awesome, and plausible. I could definitely see this game being a critique on human behavior similar to Bioshock, but we'll likely have to wait for launch to find out for ourselves. I'll certainly be picking up a copy when I can!