the reason why the fallout story is very flexible on a any place no context story is because each individual vault has its own story, and stories are hyper regionalistic. so while all regions may share the same start (nuclear fallout of course) and prewar tech, what happens after is up to the writers imagination, as long as a writer doesnt pick an already existing vault number that already has a rule.
minor lore spoilers ahead: each vault was not built the same, all were a major experiment and had different conditions to see how humanity would adapt to different conditions presented to them.
this is why fallout is super flexible on where a story can start, game, or show wise. for example of something that won’t be in a game or show, Vault 68 was an experiment where what would happen if you put 1 woman, and 999 men in a bunker. Vault 69 was what would happen if you had 1 man, and 999 women in a bunker.