Little Lamplight isn't that incoherent, they living near supermutants and continue living is incoherent, but to the people that question "Where do new kids come from then?" well people from Little Lamplight are expeled after they turn 18, but women por girls don't start ovulating and being able to egt pregnant when tey are 18, they start when they are like 13, some start even earlier.
On the Bomb, the question should not be why the brotherhood on the pentagon didn't try to salvage it, but why The Outcasts didn't raid the city, the game makes it clear (wheter you like it or not) that the capital wasteland BoS has rebeled and its using their equipment to try and help the wasteland. There are other things that are increidbly dumb, some towns seem to be written as if only mere decades had passes since the war instead of 200, like Minefield and the town of cannibals.
With Little Lamplight they could have done somethign more sinister, the camp is located outside the mutant factory, insted of having them separated by a wall of rocks they could have something more connected. The captial Mutants are dumber than the Core region Mutants but there seems to be some smart ones like Fawkes. My idea woudl have been, the Mutants and the kids being in some kind of agreement, the kids represent an endless supply of people to turn into mutants, and they are kids, they are easy to manipulate, so when a Littlelamplighter tunrs 18 or a "mungo" is the sing of their peregrination into becoming mutants, Mugno could be the way they call the mutants, in exchange of this the Mutants continue guarding the kids, the Lone Wanderer would enter Little lamp light and observe the weird conduct of the kids sending the "mungos" to the caves in peregrination and decide to investigate, thus uncovering the secret of the mutants, riding the cave of Mutants then would mean the doom of Little Lamplight and then you could either lead the slavers into the caves now that the mutant threat no longer exists, or lead the BoS there and they woudl take the kids as initiates.